@Book{ ANON80, Author = { }, Title = { {H}armonic analysis, {I}raklion 1978 }, Editor = { N.C. Petridis and S.K. Pichorides and N. Varopoulos }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 781 }, Series = { Lecture Notes in Math. }, Year = { 1980 } } @Book{ ANON82, Author = { }, Title = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Book{ ANON83, Author = { }, Title = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, N.J. }, Volume = { 103 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Book{ ANON85, Author = { }, Title = { {H}armonic {M}appings and {M}inimal {I}mmersions, {M}ontecatini 1984 }, Editor = { E. Giusti }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1161 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Book{ ANON88, Author = { }, Title = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Year = { 1988 } } @Book{ ANON93, Author = { }, Title = { {M}inimal surfaces }, Editor = { A.T. Fomenko }, Publisher = { American Math.\ Soc. }, Address = { Providence RI }, Volume = { 15 }, Series = { Adv.\ Soviet Math. }, Year = { 1993 } } @Book{ ANON94, Author = { }, Title = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ IanAMP95, Author = { S .Ianus and A.M.Pastore }, Title = { {H}armonic maps on metric contact manifolds }, Journal = { Ann.\ Math.\ Blaise Pascal }, Volume = { 2 }, Pages = { 43-53 }, Year = { 1995 } } @Article{ Abb82, Author = { R.B. Abbott }, Title = { {E}lliptic solutions of {${C}{P}^{n-1}$} models and their properties }, Journal = { Z. Phys. }, Volume = { C 15 }, Pages = { 51-59 }, Year = { 1982 } } @Article{ Abe82, Author = { N. Abe }, Title = { {O}n generalized total curvatures and conformal mappings }, Journal = { Hiroshima Math.\ J. }, Volume = { 12 }, Pages = { 203-207 }, Year = { 1982 } } @Article{ Abr83, Author = { U. Abresch }, Title = { {I}soparametric hypersurfaces with four or six distinct principal curvatures }, Journal = { Math.\ Ann. }, Volume = { 264 }, Pages = { 283-302 }, Year = { 1983 } } @Article{ Abr87, Author = { U. Abresch }, Title = { {C}onstant mean curvature tori in terms of elliptic functions }, Journal = { J. Reine Angew.\ Math. }, Volume = { 374 }, Pages = { 169-192 }, Year = { 1987 } } @Incollection{ Abr87A, Author = { U. Abresch }, Title = { {O}ld and new periodic solution of the sinh-{G}ordon equation }, Booktitle = { {S}em. on non-linear partial differential equations }, Publisher = { Vieweg }, Year = { 1987 } } @Article{ AbrLan86, Author = { U. Abresch and J. L{\"a}nger }, Title = { {T}he normalized curve shortening flow and homothetic solutions }, Journal = { J. Differential Geom. }, Volume = { 23 }, Pages = { 175-196 }, Year = { 1986 } } @Incollection{ AdaSun84, Author = { T. Adachi and T. Sunada }, Title = { {G}eometric bounds for the number of certain harmonic maps }, Booktitle = { {D}ifferential {G}eometry of {S}ubmanifolds }, Editor = { K. Kenmotsu }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1090 }, Pages = { 24-36 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ AdaSun85, Author = { T. Adachi and T. Sunada }, Title = { {E}nergy spectrum of certain harmonic mappings }, Journal = { Compositio Math. }, Volume = { 56 }, Pages = { 153-170 }, Year = { 1985 } } @Article{ AdaSim88, Author = { D. Adams and L. Simon }, Title = { {R}ates of asymptotic convergence near isolated singularities of geometric extrema }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 37 }, Pages = { 225-254 }, Year = { 1988 } } @Article{ Ada82, Author = { J.F. Adams }, Title = { {M}aps from a surface to the projective plane }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 14 }, Pages = { 533-534 }, Year = { 1982 } } @Article{ AdaFre91, Author = { S. Adams and A. Freire }, Title = { {N}onnegatively curved leaves in foliations }, Journal = { J. Differential Geom. }, Volume = { 34 }, Pages = { 681-700 }, Year = { 1991 } } @Misc{ AdaHer, Author = { S. Adams and L. Her{\'n}andez }, Title = { {A} foliated metric rigidity theorem for higher rank irreducible symmetric spaces } } @Article{ AdaStu93, Author = { S. Adams and G. Stuck }, Title = { {S}plitting of nonnegatively curved leaves in minimal sets of foliations }, Journal = { Duke Math.\ J. }, Volume = { 71 }, Pages = { 71-92 }, Year = { 1993 } } @Article{ Ade75, Author = { J. Adem }, Title = { {C}onstruction of some normed maps }, Journal = { Bol.\ Soc.\ Mat.\ Mexicana }, Volume = { 20 }, Pages = { 59-75 }, Year = { 1975 } } @Article{ Ade80, Author = { J. Adem }, Title = { {O}n the {H}urwitz problem over an arbitrary field, {I} }, Journal = { Bol.\ Soc.\ Mat.\ Mexicana }, Volume = { 25 }, Pages = { 29-5 }, Year = { 1980 } } @Article{ Ait86, Author = { A.R. Aithal }, Title = { {H}armonic maps from {${S}^2$} to {${G}_2({\bf {C}}^5)$} }, Journal = { J. London Math.\ Soc. }, Volume = { 32 }, Pages = { 572-576 }, Year = { 1986 } } @Article{ Ait86A, Author = { A.R. Aithal }, Title = { {H}armonic maps from {${S}^2$} to {${\bf {H}}{P}^2$} }, Journal = { Osaka J. Math. }, Volume = { 23 }, Pages = { 255-270 }, Year = { 1986 } } @Article{ AitNag93, Author = { A.R. Aithal and D.S. Nagaraj }, Title = { {S}plitting types of holomorphic bundles associated with some harmonic maps }, Journal = { Comm.\ Algebra }, Volume = { 21 }, Pages = { 3727-3731 }, Year = { 1993 } } @Unpublished{ AiyAku, Author = { R. Aiyama and K. Akutagawa }, Title = { {K}enmotsu-{B}ryant type representation formulas for constant mean curvature surfaces in {${\bf {H}}^3(-c^2)$} and {${S}^3_1(c^2)$} }, Note = { preprint } } @Unpublished{ AkdGooPer, Author = { K.G. Akdiniz and M. Goodman and R. Percacci }, Title = { {M}onopoles and twisted {$\sigma$}-models }, Note = { Preprint } } @Misc{ Aki, Author = { F.F. Aki-Khuzam }, Title = { {A} one-parameter family of minimal surfaces with four planar ends } } @Misc{ Aku, Author = { K. Akutagawa }, Title = { {A} {L}iouville-type property for harmonic maps with finite polynomial growth dilatation } } @Incollection{ Aku89, Author = { K. Akutagawa }, Title = { {T}he {D}irichlet problem at infinity for harmonic mappings between {H}adamard manifold }, Booktitle = { {G}eometry of {M}anifolds }, Publisher = { Academic Press }, Address = { New York }, Pages = { 59-70 }, Year = { 1989 } } @Incollection{ Aku93, Author = { K. Akutagawa }, Title = { {H}armonic maps between unbounded convex polyhedra in hyperbolic spaces }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 147-150 }, Year = { 1993 } } @Article{ Aku94, Author = { K. Akutagawa }, Title = { {H}armonic diffeomorphisms of the hyperbolic plane }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 342 }, Pages = { 325-342 }, Year = { 1994 } } @Article{ Aku96, Author = { K. Akutagawa }, Title = { {H}armonic maps between hyperbolic spaces }, Journal = { Sugaku }, Volume = { 48 }, Pages = { 128-141 }, Note = { (Japanese) }, Year = { 1996 } } @Article{ AkuNis90, Author = { K. Akutagawa and S. Nishikawa }, Title = { {T}he {G}auss map and spacelike surfaces with prescribed mean curvature in {M}inkowski {$3$}-space }, Journal = { T\^ohoku Math.\ J. }, Volume = { 42 }, Pages = { 67-82 }, Year = { 1990 } } @Incollection{ AkuNisTac93, Author = { K. Akutagawa and S. Nishikawa and A. Tachikawa }, Title = { {H}armonic maps of unbounded convex polygons in the hyperbolic plane }, Booktitle = { {G}eometry and its applications ({Y}okohama, 1991) }, Publisher = { World Sci. }, Address = { River Edge, NJ }, Pages = { 17-19 }, Year = { 1993 } } @Article{ AkuNisTac94, Author = { K. Akutagawa and S. Nishikawa and A. Tachikawa }, Title = { {H}armonic maps between unbounded convex polyhedra in hyperbolic spaces }, Journal = { Invent.\ Math. }, Volume = { 115 }, Pages = { 391-404 }, Year = { 1994 } } @Article{ AkuTac93, Author = { K. Akutagawa and A. Tachikawa }, Title = { {N}onexistence results for harmonic maps between non-compact complete {R}iemannian manifolds }, Journal = { Tokyo J. Math. }, Volume = { 16 }, Pages = { 131-145 }, Year = { 1993 } } @Article{ Alb64, Author = { S.I. Al'ber }, Title = { {O}n {$n$}-dimensional problems in the calculus of variations in the large }, Journal = { Soviet Math.\ Dokl. }, Volume = { 5 }, Pages = { 700-704 }, Year = { 1964 } } @Article{ Alb68, Author = { S.I. Al'ber }, Title = { {S}paces of mappings into a manifold with negative curvature }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 178 }, Pages = { 13-16 }, Year = { 1968 } } @Article{ Alb70, Author = { S.I. Al'ber }, Title = { {T}he topology of functional manifolds and the calculus of variations in the large }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 25 }, Number = { 4 }, Pages = { 57-122 }, Year = { 1970 } } @Article{ AleGra93, Author = { D.V. Alekseevksy and M.M. Graev }, Title = { {${G}$}-structures of twistor type and their twistor spaces }, Journal = { J. Geom.\ Phys. }, Volume = { 10 }, Pages = { 203-229 }, Year = { 1993 } } @Article{ AleBis74, Author = { S. Alexander and R.L. Bishop }, Title = { {C}onvex-supporting domains on spheres }, Journal = { Illinois J. Math. }, Volume = { 18 }, Pages = { 31-47 }, Year = { 1974 } } @Article{ Ale95, Author = { F. Alexandre }, Title = { {U}niqueness for the harmonic map flow in two dimensions }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 3 }, Pages = { 95-105 }, Year = { 1995 } } @Article{ Ale62, Author = { A.D. Alexandrov }, Title = { {A} characteristic property of spheres }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 58 }, Pages = { 303-315 }, Year = { 1962 } } @Incollection{ Ale62A, Author = { A.D. Alexandrov }, Title = { {U}niqueness theorems for surfaces in the large, {V} }, Booktitle = { {N}ine papers on topology, {L}ie groups and differential equations }, Volume = { 21 }, Pages = { 412-416 }, Series = { Amer.\ Math.\ Soc.\ Transl.\ Ser.\ 2 }, Year = { 1962 } } @Incollection{ Alm93, Author = { L. Almeida }, Title = { {E}verywhere discontinuous generalized harmonic maps into {${S}^1$} }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 423-426 }, Year = { 1993 } } @Article{ Alm95, Author = { L. Almeida }, Title = { {T}he regularity problem for generalized harmonic maps into homogeneous spaces }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 9 }, Pages = { 193-242 }, Year = { 1995 } } @Article{ Alm66, Author = { F.J. Almgren }, Title = { {S}ome interior regularity theorems for minimal surfaces and an extension of {B}ernstein's theorem }, Journal = { Ann.\ of Math. }, Volume = { 84 }, Pages = { 277-292 }, Year = { 1966 } } @Incollection{ AlmBroLie88, Author = { F.J. Almgren and W. Browder and E.H. Lieb }, Title = { {C}o-area, liquid crystals, and minimal surfaces }, Booktitle = { {P}artial differential equations, proceedings, 1986 }, Editor = { S.S. Chern }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1306 }, Pages = { 1-12 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Incollection{ AlmLie, Author = { F.J. Almgren and E.H. Lieb }, Title = { {H}ow many singularities can there be in an energy minimizing map from the ball to the sphere }, Booktitle = { {I}deas and methods in mathematical analysis, stochastics and applications ({O}slo, 1988) }, Publisher = { Cambridge University Press }, Address = { Cambridge }, Pages = { 394-408 } } @Article{ AlmLie87, Author = { F.J. Almgren and E.H. Lieb }, Title = { {S}ingularities of energy minimizing maps from the ball to the sphere }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 17 }, Pages = { 304-306 }, Year = { 1987 } } @Article{ AlmLie88, Author = { F.J. Almgren and E.H. Lieb }, Title = { {S}ingularities of energy minimizing maps from the ball to the sphere }, Journal = { Ann.\ of Math. }, Volume = { 128 }, Pages = { 483-530 }, Year = { 1988 } } @Incollection{ AlmLie90, Author = { F.J. Almgren and E.H. Lieb }, Title = { {C}ounting singularities in liquid crystals }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 17-35 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Article{ AlmSchSim77, Author = { F.J. Almgren and R. Schoen and L. Simon }, Title = { {R}egularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals }, Journal = { Acta Math. }, Volume = { 139 }, Pages = { 217-265 }, Year = { 1977 } } @Article{ AlmSim79, Author = { F.J. Almgren and L. Simon }, Title = { {E}xistence of embedded solutions to {P}lateau's problem }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 6 }, Pages = { 447-495 }, Year = { 1979 } } @Article{ Alo, Author = { F. Alouges }, Title = { {U}n sch{\'e}ma num{\'e}rique pour le calcul d'applications harmoniques de {${\bf {R}}^3$} dans la sph{\`e}re }, Journal = { C. R. Acad.\ Sci.\ Paris S\'er.\ I Math. }, Volume = { 311 }, Pages = { 565-570 } } @Incollection{ Alo90, Author = { F. Alouges }, Title = { {U}n algorithme qui d{\'e}croit s{\^u}rement l{\'e}nergie des cristaux liquides }, Booktitle = { {T}h{\`e}se, {U}niversit{\'e} de {P}aris-{S}ud }, Year = { 1990 } } @Incollection{ Alo91, Author = { F. Alouges }, Title = { {A}n energy-decreasing algorithm for harmonic maps }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 1-13 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Article{ Alt72, Author = { H.W. Alt }, Title = { {V}erzweigungspunkte von {${H}$}-{F}l\"achen, {I} }, Journal = { Math.\ Z. }, Volume = { 127 }, Pages = { 333-362 }, Year = { 1972 } } @Article{ Alt73, Author = { H.W. Alt }, Title = { {V}erzweigungspunkte von {${H}$}-{F}l\"achen, {I}{I} }, Journal = { Math.\ Ann. }, Volume = { 201 }, Pages = { 33-55 }, Year = { 1973 } } @Misc{ AltTom, Author = { H.W. Alt and F. Tomi }, Title = { {R}egularity and finiteness of solutions to the free boundary problem for minimal surfaces. } } @Article{ AlvFre81, Author = { L. Alvarez-Gaume and D.Z. Freedman }, Title = { {G}eometrical structure and ultraviolet finiteness in the supersymmetric {$\sigma$}-model }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 80 }, Pages = { 443-451 }, Year = { 1981 } } @Article{ AlvFre83, Author = { L. Alvarez-Gaume and D.Z. Freedman }, Title = { {P}otential for the supersymmetric nonlinear {$\sigma$}-model }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 91 }, Pages = { 87-101 }, Year = { 1983 } } @Article{ Alv90, Author = { J.A. Alvarez~L{\'o}pez }, Title = { {O}n {R}iemannian foliations with minimal leaves }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 40 }, Pages = { 163-176 }, Year = { 1990 } } @Article{ Ami75, Author = { J.A. Aminov }, Title = { {O}n the problem of stability of a minimal surface in a {R}iemannian space of positive curvature }, Journal = { Soviet Math.\ Dokl. }, Volume = { 16 }, Pages = { 1278-1281 }, Year = { 1975 } } @Article{ Ami76, Author = { J.A. Aminov }, Title = { {T}he instability of a minimal surface in an {$n$}-dimensional {R}iemannian space of positive curvature }, Journal = { Math.\ Sb.\ (N.S.) }, Volume = { 100 (142) }, Pages = { 400-419, 478 }, Year = { 1976 } } @Book{ AmoBurCor96, Author = { J. Amor\'os and M. Burger and K. Corlette and D. Kotschick and D. Toledo }, Title = { {F}undamental groups of compact {K}\"ahler manifolds }, Publisher = { American Math.\ Soc. }, Address = { Providence, RI }, Volume = { 44 }, Series = { Math.\ Surveys Monogr. }, Year = { 1996 } } @Misc{ Ana, Author = { C.K. Anand }, Title = { {A} closed form for unitons } } @Misc{ AnaA, Author = { C.K. Anand }, Title = { {W}ard's solitons } } @Article{ Ana95, Author = { C.K. Anand }, Title = { {U}niton bundles }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 3 }, Pages = { 371-419 }, Year = { 1995 } } @Article{ Ana96, Author = { C.K. Anand }, Title = { {U}nitons and their moduli }, Journal = { Electron.\ Res.\ Announc.\ Amer.\ Math.\ Soc. }, Volume = { 2 }, Pages = { 7-16 }, Year = { 1996 } } @Article{ AndHenHof88, Author = { D.M. Anderson and C.S. Henke and D.A. Hoffman and E.L. Thomas }, Title = { {P}eriodic area-minimizing surfaces in block copolymers }, Journal = { Nature }, Volume = { 334 }, Pages = { 598-601 }, Year = { 1988 } } @Book{ And, Author = { I.M. Anderson }, Title = { {T}he variational bicomplex }, Publisher = { Academic Press }, Note = { (to appear) } } @Article{ And78, Author = { I.M. Anderson }, Title = { {I}n the structure of divergence free tensors }, Journal = { J. Math.\ Phys. }, Volume = { 19 }, Pages = { 2570-2575 }, Year = { 1978 } } @Article{ And84, Author = { I.M. Anderson }, Title = { {N}atural variational principles on {R}iemannian manifolds }, Journal = { Ann.\ of Math. }, Volume = { 120 }, Pages = { 329-370 }, Year = { 1984 } } @Article{ And84A, Author = { I.M. Anderson }, Title = { {V}ariational principles for second-order quasi-linear scalar equations }, Journal = { J. Differential Equations }, Volume = { 51 }, Pages = { 1-47 }, Year = { 1984 } } @Article{ And88, Author = { I.M. Anderson }, Title = { {A}spects of the inverse problem to the calculus of variations }, Journal = { Arch.\ Math.\ (Brno) }, Volume = { 24 }, Pages = { 181-202 }, Year = { 1988 } } @Incollection{ And92, Author = { I.M. Anderson }, Title = { {I}ntroduction to the variational bicomplex }, Booktitle = { {M}athematical aspects of classical field theory }, Editor = { M. Gotay and V.E. Moncrief and J.E. Marsden }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 132 }, Pages = { 51-73 }, Series = { Contemp.\ Math. }, Year = { 1992 } } @Article{ AndDuc80, Author = { I.M. Anderson and T. Duchamp }, Title = { {O}n the existence of global variational principles }, Journal = { Amer.\ J. Math. }, Volume = { 102 }, Pages = { 781-868 }, Year = { 1980 } } @Book{ AndTho92, Author = { I.M. Anderson and G. Thompson }, Title = { {T}he inverse problem of the calculus of variations for ordinary differential equations }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 473 }, Series = { Mem.\ Amer.\ Math.\ Soc. }, Year = { 1992 } } @Misc{ AndA, Author = { M.T. Anderson }, Title = { {T}he compactification of a minimal submanifold in {E}uclidean space by the {G}auss map } } @Article{ And82, Author = { M.T. Anderson }, Title = { {C}omplete minimal surfaces in hyperbolic space }, Journal = { Invent.\ Math. }, Volume = { 69 }, Pages = { 477-494 }, Year = { 1982 } } @Article{ And83, Author = { M.T. Anderson }, Title = { {C}omplete minimal hypersurfaces in hyperbolic {$n$}-manifolds }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 58 }, Pages = { 264-290 }, Year = { 1983 } } @Article{ And83A, Author = { M.T. Anderson }, Title = { {T}he {D}irichlet problem at infinity for manifolds of negative curvature }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 701-721 }, Year = { 1983 } } @Article{ And83B, Author = { M.T. Anderson }, Title = { {O}n area-minimizing hypersufaces in manifolds of non-negative curvature }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 32 }, Pages = { 745-760 }, Year = { 1983 } } @Article{ And85, Author = { M.T. Anderson }, Title = { {C}urvature estimates for minimal surfaces in {$3$}-manifolds }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 18 }, Pages = { 89-105 }, Year = { 1985 } } @Incollection{ And86, Author = { M.T. Anderson }, Title = { {L}ocal estimates for minimal submanifolds in dimensions greater than two }, Booktitle = { {G}eometric {M}easure {T}heory and the {C}alculus of {V}ariations }, Editor = { W.K. Allard and F.J. Almgren }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 44 }, Pages = { 131-137 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Article{ AndSch85, Author = { M.T. Anderson and R. Schoen }, Title = { {P}ositive harmonic functions on complete manifolds of negative curvature }, Journal = { Ann.\ of Math. }, Volume = { 121 }, Pages = { 429-461 }, Year = { 1985 } } @Article{ AndVes65, Author = { A. Andreotti and E. Vesentini }, Title = { {C}arleman estimates for the {L}aplace--{B}eltrami equation on complex manifolds }, Journal = { Inst.\ Hautes \'Etudes Sci.\ Publ.\ Math. }, Volume = { 25 }, Pages = { 81-130 }, Year = { 1965 } } @Article{ Ang90, Author = { S.B. Angenent }, Title = { {P}arabolic equations for curves on surface {I} }, Journal = { Ann.\ of Math. }, Volume = { 132 }, Pages = { 451-483 }, Year = { 1990 } } @Article{ Ang91, Author = { S.B. Angenent }, Title = { {O}n the formation of singularities in the curve shortening problem }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 601-633 }, Year = { 1991 } } @Article{ Ang91A, Author = { S.B. Angenent }, Title = { {P}arabolic equations for curves on surface {I}{I} }, Journal = { Ann.\ of Math. }, Volume = { 133 }, Pages = { 171-215 }, Year = { 1991 } } @Article{ Ang92, Author = { S.B. Angenent }, Title = { {S}ome recent results on mean curvature flow }, Journal = { Rec.\ Adv.\ in PDE }, Pages = { 1-18 }, Year = { 1992 } } @Article{ AnsFre94, Author = { D. Anselmi and P. Fr{\'e} }, Title = { {T}opological {$\sigma$}-models in four dimensions and triholomorphic maps }, Journal = { Nuclear Phys.\ B }, Volume = { 416 }, Pages = { 255-300 }, Year = { 1994 } } @Article{ AntPie87, Author = { J.P. Antoine and B. Piette }, Title = { {C}lassical non-linear {$\sigma$} models in {G}rassmannian manifolds of compact or non-compact type }, Journal = { J. Math.\ Phys. }, Volume = { 28 }, Pages = { 2753-2762 }, Year = { 1987 } } @Article{ AntPie88, Author = { J.P. Antoine and B. Piette }, Title = { {S}olutions of {E}uclidean {$\sigma$}-models on non-compact {G}rassmannian manifolds }, Journal = { J. Math.\ Phys. }, Volume = { 29 }, Pages = { 1687-1697 }, Year = { 1988 } } @Article{ AraFar94, Author = { C.S. Aravinda and F.T. Farrell }, Title = { {R}ank of a spherical manifolds which do not support any nonpositively curved metric }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 2 }, Pages = { 65-78 }, Year = { 1994 } } @Unpublished{ Are96, Author = { C. Arezzo }, Title = { {O}n minimal surfaces incompressible in homology and abelian varieties }, Note = { Warwick preprint }, Year = { 1996 } } @Unpublished{ Are96A, Author = { C. Arezzo }, Title = { {S}table complete minimal surfaces in hyperk\"ahler manifolds }, Note = { Genoa preprint }, Year = { 1996 } } @Unpublished{ Are96B, Author = { C. Arezzo }, Title = { {T}he {T}orelli and the {I}nfinitesimal {T}orelli {T}heorems for {M}inimal surfaces }, Note = { Warwick preprint }, Year = { 1996 } } @Article{ Ari88, Author = { M. Arik }, Title = { {G}rassmannian {$\sigma$}-models and strings }, Journal = { J. Math.\ Phys. }, Volume = { 29 }, Pages = { 594-598 }, Year = { 1988 } } @Article{ Aro67, Author = { G. Aronsson }, Title = { {E}xtension of functions satisfying {L}ipschitz conditions }, Journal = { Ark.\ Mat. }, Volume = { 6 }, Pages = { 551-561 }, Year = { 1967 } } @Article{ Aro57, Author = { N. Aronszajn }, Title = { {A} unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order }, Journal = { J. Math.\ Pures Appl. }, Volume = { 9 }, Pages = { 235-249 }, Year = { 1957 } } @Article{ AroKrzSza62, Author = { N. Aronszajn and A. Krzywicki and J. Szarski }, Title = { {A} unique continuation theorem for exterior differential forms on {R}iemannian manifolds }, Journal = { Ark.\ Mat. }, Volume = { 4 }, Pages = { 417-453 }, Year = { 1962 } } @Article{ ArsJacSai88, Author = { G. Arsenault and M. Jacques and Y. Saint-Aubin }, Title = { {C}ollapse and exponentiation of infinite symmetry algebras of {E}uclidean projective and grassmannian sigma models }, Journal = { J. Math.\ Phys. }, Volume = { 29 }, Pages = { 1465-1471 }, Year = { 1988 } } @Incollection{ ArsJacSai88A, Author = { G. Arsenault and M. Jacques and Y. Saint-Aubin }, Title = { {E}nlarging the {${S}{U}(n+1)$} symmetry group of the {E}uclidean {${C}{P}^n$} models to {${S}{L}(n+1,{C})$} }, Booktitle = { {C}{A}{P}-{N}{S}{E}{R}{C} {S}ummer {I}nstitute in {T}heoretical {P}hysics {V}ol {I}{I} ({E}dmonton {A}{B} 1987) }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 147-160 }, Year = { 1988 } } @Incollection{ ArsJacSai88B, Author = { G. Arsenault and M. Jacques and Y. Saint-Aubin }, Title = { {T}he symmetry group of the {E}uclidean {${C}{P}^n$} model as the invariance group of bilinear forms }, Booktitle = { {G}roup theoretic methods in physics ({V}arna, 1987) }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New-York }, Volume = { 313 }, Pages = { 507-512 }, Series = { Lecture Notes in Phys. }, Year = { 1988 } } @Article{ ArsSai89, Author = { G. Arsenault and Y. Saint-Aubin }, Title = { {T}he hidden symmetry of {${U}(n)$} principal {$\sigma$}-models revisited {I} }, Journal = { Nonlinearity }, Volume = { 2 }, Pages = { 571-591 }, Year = { 1989 } } @Article{ ArsSai89A, Author = { G. Arsenault and Y. Saint-Aubin }, Title = { {T}he hidden symmetry of {${U}(n)$} principal {$\sigma$}-models revisited {I}{I} }, Journal = { Nonlinearity }, Volume = { 2 }, Pages = { 593-607 }, Year = { 1989 } } @Article{ Asa96, Author = { K. Asai }, Title = { {T}he heat flows of harmonic maps from {${S}^2$} to {${S}^2$} }, Journal = { J. Math.\ Sci.\ Univ.\ Tokyo }, Volume = { 3 }, Pages = { 1--13 }, Year = { 1996 } } @Article{ Asp84, Author = { A.C. Asperti }, Title = { {M}inimal surfaces with constant normal curvature }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 36 }, Pages = { 375-386 }, Year = { 1984 } } @Article{ Asp89, Author = { A.C. Asperti }, Title = { {G}eneric minimal surfaces }, Journal = { Math.\ Z. }, Volume = { 200 }, Pages = { 181-186 }, Year = { 1989 } } @Article{ Ati84, Author = { M.F. Atiyah }, Title = { {I}nstantons in two and four dimensions }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 93 }, Pages = { 437-451 }, Year = { 1984 } } @Article{ AtiBotPat73, Author = { M.F. Atiyah and R. Bott and V.K. Patodi }, Title = { {O}n the heat equation and the index theorem }, Journal = { Invent.\ Math. }, Volume = { 19 }, Pages = { 279-330 }, Year = { 1973 } } @Article{ AtiHitSin78, Author = { M.F. Atiyah and N.J. Hitchin and I.M. Singer }, Title = { {S}elf-duality in four-dimensional {R}iemannian geometry }, Journal = { Proc.\ Roy.\ Soc.\ London Ser.\ A }, Volume = { 362 }, Pages = { 425-461 }, Year = { 1978 } } @Incollection{ AtiPre83, Author = { M.F. Atiyah and A.N. Pressley }, Title = { {C}onvexity and loop groups }, Booktitle = { {A}rithmetic and {G}eometry }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 36 }, Pages = { 33-64 }, Series = { Progr.\ Math. }, Year = { 1983 } } @Misc{ AvcZlo, Author = { Y. Avci and E. Z{\l}otkiewicz }, Title = { {O}n harmonic univalent mappings } } @Article{ AveLin88, Author = { M. Avellaneda and F-H Lin }, Title = { {F}onctions quasi affines et minimisation de {$\int {\vert \nabla u \vert}^p$} }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 306 }, Pages = { 355-358 }, Year = { 1988 } } @Misc{ Avi, Author = { P. Avil{\'e}s }, Title = { {O}n the regularity of minimising harmonic maps } } @Misc{ AviChoMic, Author = { P. Avil{\'e}s and H.I. Choi and M.J. Micallef }, Title = { {T}he behavior at infinity of harmonic maps between complete negatively curved manifolds } } @Misc{ AviChoMicA, Author = { P. Avil{\'e}s and H.I. Choi and M.J. Micallef }, Title = { {B}oundary behavior of solutions of certain elliptic systems of {P}.{D}.{E}. } } @Incollection{ AviChoMic89, Author = { P. Avil{\'e}s and H.I. Choi and M.J. Micallef }, Title = { {T}he {D}irichlet problem and {F}atou's theorem for harmonic maps }, Booktitle = { {R}ecent developments in geometry }, Editor = { S.Y. Cheng and H. Choi and R.E. Greene }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 101 }, Pages = { 79-86 }, Series = { Contemp.\ Math. }, Year = { 1989 } } @Article{ AviChoMic91, Author = { P. Avil{\'e}s and H.I. Choi and M.J. Micallef }, Title = { {B}oundary behavior of harmonic maps on non-smooth domains and complete negatively curved manifolds }, Journal = { J. Funct.\ Anal. }, Volume = { 99 }, Pages = { 293-331 }, Year = { 1991 } } @Misc{ AviGig, Author = { P. Avil{\'e}s and Y. Giga }, Title = { {P}artial regularity of least gradient mappings } } @Article{ BabBob93, Author = { M. Babich and A.I. Bobenko }, Title = { {W}illmore tori with umbilic lines and minimal surfaces in hyperbolic space }, Journal = { Duke Math.\ J. }, Volume = { 72 }, Pages = { 151-185 }, Year = { 1993 } } @Unpublished{ Bah88, Author = { A. Bahy-El-Dien }, Title = { {O}n the construction of harmonic two-spheres in complex hypersurfaces and quaternionic projective spaces }, Note = { Thesis, Leeds Univ. }, Year = { 1988 } } @Article{ BahWoo89, Author = { A. Bahy-El-Dien and J.C. Wood }, Title = { {T}he explicit construction of all harmonic two-spheres in {${G}_2({\bf {R}}^n)$} }, Journal = { J. Reine Angew.\ Math. }, Volume = { 398 }, Pages = { 36-66 }, Year = { 1989 } } @Article{ BahWoo91, Author = { A. Bahy-El-Dien and J.C. Wood }, Title = { {T}he explicit construction of all harmonic two-spheres in quaternionic projective spaces }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 62 }, Pages = { 202-224 }, Year = { 1991 } } @Article{ BaiKou83, Author = { C. Baikoussis and T. Koufogiorgos }, Title = { {H}armonic maps into a cone }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 40 }, Pages = { 372-376 }, Year = { 1983 } } @Article{ BaiKou85, Author = { C. Baikoussis and T. Koufogiorgos }, Title = { {A} theorem on the tension field }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 93 }, Pages = { 321-324 }, Year = { 1985 } } @Misc{ Bai, Author = { P. Baird }, Title = { {C}onformal foliations by circles of {E}uclidean 3-space } } @Unpublished{ Bai81, Author = { P. Baird }, Title = { {H}armonic maps with symmetry, harmonic morphisms, and deformation of metrics }, Note = { Warwick Ph.D Thesis }, Year = { 1981 } } @Book{ Bai83, Author = { P. Baird }, Title = { {H}armonic maps with symmetry, harmonic morphisms, and deformation of metrics }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 87 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1983 } } @Unpublished{ Bai83A, Author = { P. Baird }, Title = { {O}n a higher dimensional analogue of {N}eumann motion and harmonic maps into spheres }, Note = { Preprint, MIT }, Year = { 1983 } } @Incollection{ Bai83B, Author = { P. Baird }, Title = { {S}ome aspects of theoretical physics relating to harmonic maps }, Booktitle = { {D}ifferential {G}eometry and {M}athematical {P}hysics }, Editor = { M. Cahen and M. de~Wilde and L. Lemaire and L. Vanhecke }, Publisher = { Reidel }, Address = { Dortrecht, Holland, London }, Volume = { 3 }, Pages = { 97-104 }, Series = { Math.\ Phys.\ Stud. }, Year = { 1983 } } @Article{ Bai84, Author = { P. Baird }, Title = { {H}armonic morphisms onto {R}iemann surfaces---some classification results }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 8 }, Pages = { 91-100 }, Year = { 1984 } } @Unpublished{ Bai84A, Author = { P. Baird }, Title = { {O}n the classification of harmonic morphisms with totally geodesic fibre from an open subset of {E}uclidean space onto a {R}iemann surface }, Note = { A.N.U. preprint }, Year = { 1984 } } @Article{ Bai85, Author = { P. Baird }, Title = { {T}he {G}auss map of a submersion }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 10 }, Pages = { 8-24 }, Year = { 1985 } } @Article{ Bai87, Author = { P. Baird }, Title = { {B}ernstein theorems for harmonic morphisms }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 12 }, Pages = { 17-23 }, Year = { 1987 } } @Article{ Bai87A, Author = { P. Baird }, Title = { {H}armonic morphisms onto {R}iemann surfaces and generalized analytic functions }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 37 }, Pages = { 135-173 }, Year = { 1987 } } @Incollection{ Bai88, Author = { P. Baird }, Title = { {B}ernstein {T}heorems for harmonic morphisms }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 3-13 }, Year = { 1988 } } @Article{ Bai90, Author = { P. Baird }, Title = { {H}armonic morphisms and circle actions on {$3$}- and {$4$}-manifolds }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 40 }, Pages = { 177-212 }, Year = { 1990 } } @Article{ Bai92, Author = { P. Baird }, Title = { {A} {B}ochner technique for harmonic mappings from a {$3$}-manifold to a surface }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 10 }, Pages = { 63-72 }, Year = { 1992 } } @Article{ Bai92A, Author = { P. Baird }, Title = { {A} {H}amiltonian system on hyperbolic space and associated harmonic maps }, Journal = { Phys.\ D }, Volume = { 59 }, Pages = { 349-364 }, Year = { 1992 } } @Article{ Bai92B, Author = { P. Baird }, Title = { {R}iemannian twistors and {H}ermitian structures on low-dimensional space forms }, Journal = { J. Math.\ Phys. }, Volume = { 33 }, Pages = { 3340-3355 }, Year = { 1992 } } @Article{ Bai93, Author = { P. Baird }, Title = { {S}tatic fields on three-dimensional space forms in terms of contour integrals of twistor functions }, Journal = { Phys.\ Lett.\ A }, Volume = { 179 }, Pages = { 279-283 }, Year = { 1993 } } @Incollection{ BaiEel81, Author = { P. Baird and J. Eells }, Title = { {A} conservation law for harmonic maps }, Booktitle = { {G}eometry {S}ymposium. {U}trecht 1980 }, Editor = { E. Looijenga and D. Siersma and F. Takens }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 894 }, Pages = { 1-25 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Article{ BaiGud92, Author = { P. Baird and S. Gudmundsson }, Title = { {$p$}-harmonic maps and minimal submanifolds }, Journal = { Math.\ Ann. }, Volume = { 294 }, Pages = { 611-624 }, Year = { 1992 } } @Article{ BaiOu97, Author = { P. Baird and Y.L. Ou }, Title = { {H}armonic maps and morphisms from multilinear norm-preserving mappings }, Journal = { Internat.\ J. Math. }, Volume = { 8 }, Pages = { 187--211 }, Year = { 1997 } } @Article{ BaiRat92, Author = { P. Baird and A. Ratto }, Title = { {C}onservation laws, equivariant harmonic maps and harmonic morphisms }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 64 }, Pages = { 197-224 }, Year = { 1992 } } @Unpublished{ BaiWoo, Author = { P. Baird and J.C. Wood }, Title = { {W}eierstrass representations for harmonic morphisms on {E}uclidean spaces }, Note = { Leeds preprint } } @Article{ BaiWoo88, Author = { P. Baird and J.C. Wood }, Title = { {B}ernstein theorems for harmonic morphisms from {${\bf {R}}^3$} and {${S}^3$} }, Journal = { Math.\ Ann. }, Volume = { 280 }, Pages = { 579-603 }, Year = { 1988 } } @Article{ BaiWoo90, Author = { P. Baird and J.C. Wood }, Title = { {A} spinor formulation for harmonic morphisms }, Journal = { Twistor Newsletter }, Volume = { 31 }, Pages = { 29-37 }, Year = { 1990 } } @Article{ BaiWoo91, Author = { P. Baird and J.C. Wood }, Title = { {H}armonic morphisms and conformal foliations by geodesics of three-dimensional space forms }, Journal = { J. Austral.\ Math.\ Soc.\ Ser.\ A }, Volume = { 51 }, Pages = { 118-153 }, Year = { 1991 } } @Article{ BaiWoo92, Author = { P. Baird and J.C. Wood }, Title = { {T}he geometry of a pair of {R}iemannian foliations by geodesics and associated harmonic morphisms }, Journal = { Bull.\ Soc.\ Math.\ Belg. }, Volume = { 44 }, Pages = { 115-139 }, Year = { 1992 } } @Article{ BaiWoo92A, Author = { P. Baird and J.C. Wood }, Title = { {H}armonic morphisms, {S}eifert fibre spaces and conformal foliations }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 64 }, Pages = { 170-196 }, Year = { 1992 } } @Article{ BaiWoo95, Author = { P. Baird and J.C. Wood }, Title = { {H}ermitian structures and harmonic morphisms on higher dimensional {E}uclidean spaces }, Journal = { Internat.\ J. Math. }, Volume = { 6 }, Pages = { 161-192 }, Year = { 1995 } } @Incollection{ BaiWoo95A, Author = { P. Baird and J.C. Wood }, Title = { {M}onopoles, harmonic morphisms and spinor fields }, Booktitle = { {F}urther {A}dvances in {T}wistor {T}heory, {V}ol 2 }, Editor = { L.J. Mason and L.P. Hughston and P.Z. Kobak }, Publisher = { Longman Sci.\ Tech. }, Address = { Harlow }, Volume = { 232 }, Pages = { 49-62 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1995 } } @Article{ Bal82, Author = { A. Baldes }, Title = { {H}armonic mappings with partially free boundary }, Journal = { Manuscripta Math. }, Volume = { 40 }, Pages = { 255-275 }, Year = { 1982 } } @Unpublished{ Bal84, Author = { A. Baldes }, Title = { {H}armonische {A}bbildungen singul\"arer {R}iemannscher {M}annigfaltigkeiten }, Note = { Bonn Dissertation }, Year = { 1984 } } @Article{ Bal84A, Author = { A. Baldes }, Title = { {S}tability and uniqueness properties of the equator map from a ball into an ellipsoid }, Journal = { Math.\ Z. }, Volume = { 185 }, Pages = { 505-516 }, Year = { 1984 } } @Misc{ Bal85, Author = { A. Baldes }, Title = { {N}on-existence of {R}iemannian metrics with prescribed {R}icci tensor }, Year = { 1985 } } @Article{ Bal86, Author = { A. Baldes }, Title = { {D}egenerate elliptic operators, diagonal systems and variational integrals }, Journal = { Manuscripta Math. }, Volume = { 55 }, Pages = { 467-486 }, Year = { 1986 } } @Misc{ Bal, Author = { W. Ballmann }, Title = { {O}n the {D}irichlet problem at infinity for manifolds of nonpositive curvature } } @Article{ Bal78, Author = { W. Ballmann }, Title = { {D}oppelpunktfreie geschlossene {G}eod\"atische auf kompakten {F}l\"achen }, Journal = { Math.\ Z. }, Volume = { 161 }, Pages = { 41-46 }, Year = { 1978 } } @Article{ Ban84, Author = { S. Bando }, Title = { {O}n the classification of three dimensional compact {K}\"ahler manifolds of nonnegative bisectional curvature }, Journal = { J. Differential Geom. }, Volume = { 19 }, Pages = { 289-297 }, Year = { 1984 } } @Article{ BanOhn87, Author = { S. Bando and Y. Ohnita }, Title = { {M}inimal {$2$}-spheres with constant curvature in {${P}_n({\bf {C}})$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 39 }, Pages = { 477-487 }, Year = { 1987 } } @Article{ Ban93, Author = { V. Bangert }, Title = { {O}n the existence of closed geodesics on two spheres }, Journal = { Internat.\ J. Math. }, Volume = { 4 }, Pages = { 1-10 }, Year = { 1993 } } @Article{ BanOks87, Author = { R. Banuelos and B. {\O}ksendal }, Title = { {E}xit times for elliptic diffusions and {B}{M}{O} }, Journal = { Proc.\ Edinburgh Math.\ Soc. }, Volume = { 30 }, Pages = { 273-287 }, Year = { 1987 } } @Article{ BarYe92, Author = { S. Baraket and D. Ye }, Title = { {M}inimizing harmonic mappings from a surface perfored with small holes into a {R}iemannian manifold }, Journal = { Manuscripta Math. }, Volume = { 77 }, Pages = { 191-199 }, Year = { 1992 } } @Unpublished{ BarGlaTot87, Author = { D. Barbasch and J.F. Glazebrook and G. Toth }, Title = { {H}armonic maps of complex projective spaces to quotients of spheres }, Note = { Rutgers University Preprint }, Year = { 1987 } } @Article{ BarGlaTot90, Author = { D. Barbasch and J.F. Glazebrook and G. Toth }, Title = { {H}armonic maps between complex projective spaces }, Journal = { Geom.\ Dedicata }, Volume = { 33 }, Pages = { 37-50 }, Year = { 1990 } } @Article{ Bar75, Author = { J.L. Barbosa }, Title = { {O}n minimal immersions of {${S}^2$} into {${S}^{2n}$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 210 }, Pages = { 75-106 }, Year = { 1975 } } @Article{ Bar78, Author = { J.L. Barbosa }, Title = { {R}emarks on stability of minimal hypersurfaces }, Journal = { An.\ Acad.\ Brasil.\ Ci\^enc. }, Volume = { 50 }, Pages = { 295-297 }, Year = { 1978 } } @Article{ Bar79, Author = { J.L. Barbosa }, Title = { {A}n extrinsic rigidity theorem for immersions from {${S}^2$} into {${S}^n$} }, Journal = { J. Differential Geom. }, Volume = { 14 }, Pages = { 355-368 }, Year = { 1979 } } @Article{ BarDajJor, Author = { J.L. Barbosa and M. Dajczer and L.P. Jorge }, Title = { {R}igidity of minimal submanifolds in space forms }, Journal = { Math.\ Ann. }, Volume = { 267 }, Pages = { 433-437 } } @Misc{ BardoC, Author = { J.L. Barbosa and M.P. do~Carmo }, Title = { {S}tability of minimal surfaces and eigenvalues } } @Article{ BardoC76, Author = { J.L. Barbosa and M.P. do~Carmo }, Title = { {O}n the size of a minimal surface in {${\bf {R}}^3$} }, Journal = { Amer.\ J. Math. }, Volume = { 98 }, Pages = { 515-528 }, Year = { 1976 } } @Article{ BardoC80, Author = { J.L. Barbosa and M.P. do~Carmo }, Title = { {S}tability of minimal surfaces in spaces of constant curvature }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 11 }, Pages = { 1-10 }, Year = { 1980 } } @Article{ BardoC81, Author = { J.L. Barbosa and M.P. do~Carmo }, Title = { {S}tability of minimal surfaces in a {$3$}-dimensional hyperbolic space }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 36 }, Pages = { 554-557 }, Year = { 1981 } } @Article{ BardoC83, Author = { J.L. Barbosa and M.P. do~Carmo }, Title = { {H}opf's conjecture for stable minimal surfaces }, Journal = { An.\ Acad.\ Brasil.\ Ci\^enc. }, Volume = { 55 }, Pages = { 15-17 }, Year = { 1983 } } @Article{ BardoC84, Author = { J.L. Barbosa and M.P. do~Carmo }, Title = { {S}tability of hypersurfaces with constant mean curvature }, Journal = { Math.\ Z. }, Volume = { 185 }, Pages = { 339-353 }, Year = { 1984 } } @Article{ BardoCEsc88, Author = { J.L. Barbosa and M.P. do~Carmo and J. Eschenburg }, Title = { {S}tability of hypersurfaces of constant mean curvature in {R}iemannian manifolds }, Journal = { Math.\ Z. }, Volume = { 197 }, Pages = { 123-138 }, Year = { 1988 } } @Unpublished{ BarKenOsh, Author = { J.L. Barbosa and K. Kenmotsu and G. Oshikiri }, Title = { {F}oliations by hypersurfaces with constant mean curvature }, Note = { preprint } } @Article{ BarUrb81, Author = { M. Barros and F. Urbano }, Title = { {D}ifferential geometry of {${U}(p+q+r)/{U}(p)\times {U}(q)\times {U}(r)$} }, Journal = { Rend.\ Circ.\ Mat.\ Palermo }, Volume = { 30 }, Pages = { 83-96 }, Year = { 1981 } } @Article{ BarUrb87, Author = { M. Barros and F. Urbano }, Title = { {S}pectral geometry of minimal surfaces in the sphere }, Journal = { T\^ohoku Math.\ J. }, Volume = { 39 }, Pages = { 575-588 }, Year = { 1987 } } @Article{ Bar84, Author = { R. Bartnik }, Title = { {E}xistence of maximal surfaces in asymptotically flat spacetimes }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 94 }, Pages = { 155-175 }, Year = { 1984 } } @Article{ BarSim82, Author = { R. Bartnik and L. Simon }, Title = { {S}pacelike hypersurfaces with prescribed boundary values and mean curvature }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 87 }, Pages = { 131-152 }, Year = { 1982 } } @Unpublished{ BarStrYe, Author = { J. Bartz and M. Struwe and R. Ye }, Title = { {A} new approach to the {R}icci flow on {${S}^2$} }, Note = { preprint } } @Article{ BasEri94, Author = { S. Baskal and A. Eriz }, Title = { {B}\"acklund transformations for harmonic maps in two independent variables }, Journal = { Internat.\ J. Theoret.\ Phys. }, Volume = { 33 }, Pages = { 1371-1382 }, Year = { 1994 } } @Misc{ BatKeh, Author = { N.A. Batakis and A.A. Kehagris }, Title = { {C}hiral fermion compatibility induced by nonlinear sigmas } } @Misc{ Bat, Author = { D. Battig }, Title = { {W}illmore immersion, integrable systems and loop groups } } @Article{ Bee80, Author = { M.J. Beeson }, Title = { {O}n interior branch points of minimal surfaces }, Journal = { Math.\ Z. }, Volume = { 171 }, Pages = { 133-154 }, Year = { 1980 } } @Article{ Bee85, Author = { M.J. Beeson }, Title = { {T}he {$6\pi$} theorem about minimal surfaces }, Journal = { Pacific J. Math. }, Volume = { 117 }, Pages = { 17-25 }, Year = { 1985 } } @Article{ BeeTro84, Author = { M.J. Beeson and A.J. Tromba }, Title = { {T}he cusp catastrophe of {T}hom in the bifurcation of minimal surfaces }, Journal = { Manuscripta Math. }, Volume = { 46 }, Pages = { 273-308 }, Year = { 1984 } } @Incollection{ Bej88, Author = { C.-L. Bejan }, Title = { {O}n harmonic maps between semi-{R}iemannian manifolds }, Booktitle = { {X}{V}{I}{I}{I}{$^{\rm th}$} {N}at. {C}onf. {G}eo. {T}op. ({O}nadea 1987) {C}luj-{N}apoca }, Pages = { 31-34 }, Year = { 1988 } } @Article{ BelPol75, Author = { A.A. Belavin and A.M. Polyakov }, Title = { {M}etastable states of two-dimensional isotropic ferromagnets }, Journal = { JETP Lett. }, Volume = { 22 }, Pages = { 245-247 }, Year = { 1975 } } @Article{ BenCor85, Author = { V. Benci and J.-M. Coron }, Title = { {T}he {D}irichlet problem for harmonic maps from the disk into the {E}uclidean {$n$}-sphere }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 2 }, Pages = { 119-141 }, Year = { 1985 } } @Article{ Ber70, Author = { M. Berger }, Title = { {Q}uelques formules de variation pour une structure riemannienne }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 3 }, Pages = { 285-294 }, Year = { 1970 } } @Book{ BerGauMaz71, Author = { M. Berger and P. Gauduchon and E. Mazet }, Title = { {L}e spectre d'une vari\'et\'e riemannienne }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 194 }, Series = { Lecture Notes in Math. }, Year = { 1971 } } @Article{ BerGue91, Author = { M.J. Bergvelt and M.A. Guest }, Title = { {A}ctions of loop groups on harmonic maps }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 326 }, Pages = { 861-886 }, Year = { 1991 } } @Article{ BerCamDav79, Author = { A. Bernard and E.A. Cambell and A.M. Davie }, Title = { {B}rownian motion and generalized analytic and inner functions }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 29 }, Pages = { 207-228 }, Year = { 1979 } } @Article{ Ber93, Author = { F. Bernatzski }, Title = { {T}he {P}lateau-{D}ouglas problem for nonorentable minimal surfaces }, Journal = { Manuscripta Math. }, Volume = { 79 }, Pages = { 73-80 }, Year = { 1993 } } @Unpublished{ BerBolWoo, Author = { J. Berndt and J. Bolton and L.M. Woodward }, Title = { {A}lmost complex curves and {H}opf hypersurfaces in the nearly {K}{\"a}hler {$6$}-sphere }, Note = { Preprint, Durham } } @Incollection{ BerBolWoo93, Author = { J. Berndt and J. Bolton and L.M. Woodward }, Title = { {M}inimal {L}iouville surfaces }, Booktitle = { {G}eometry and topology of submanifolds {V} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 26-40 }, Year = { 1993 } } @Book{ BerTriVan95, Author = { J. Berndt and F. Tricerri and L. Vanhecke }, Title = { {G}eneralized {H}eisenberg groups and {D}amek-{R}icci harmonic spaces }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1598 }, Series = { Lecture Notes in Math. }, Year = { 1995 } } @Article{ Ber10, Author = { S. Bernstein }, Title = { {S}ur les surfaces d\'efines au moyen de leur courbure moyenne ou totale }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 27 }, Pages = { 233-256 }, Year = { 1910 } } @Article{ Ber17, Author = { S. Bernstein }, Title = { {S}ur un th\'eor\`eme de g\'eom\'etrie et son application aux \'equations aux d\'eriv\'ees partielles du type elliptique }, Journal = { Comm.\ Soc.\ Math.\ de Kharkov }, Volume = { 15 }, Pages = { 38-45 }, Year = { 1915-17 } } @Article{ Ber51, Author = { L. Bers }, Title = { {I}solated singularities of minimal surfaces }, Journal = { Ann.\ of Math. }, Volume = { 53 }, Pages = { 364-386 }, Year = { 1951 } } @Article{ Ber55, Author = { L. Bers }, Title = { {L}ocal behavior of solutions of general linear elliptic equations }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 8 }, Pages = { 473-496 }, Year = { 1955 } } @Article{ Ber56, Author = { L. Bers }, Title = { {S}urvey of local properties of solutions of elliptic partial differential equations }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 9 }, Pages = { 339-350 }, Year = { 1956 } } @Incollection{ Ber60, Author = { L. Bers }, Title = { {Q}uasiconformal mappings and {T}eichm\"uller's theorem }, Booktitle = { {A}nalytic {F}unctions }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 24 }, Pages = { 89-119 }, Series = { Princeton Math.\ Ser. }, Year = { 1960 } } @Article{ Bet88, Author = { F. Bethuel }, Title = { {A}pproximation dans des espaces de {S}obolev entre deux vari\'et\'es et groupes d'homotopie }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 307 }, Pages = { 293-296 }, Year = { 1988 } } @Unpublished{ Bet89, Author = { F. Bethuel }, Title = { {T}he approximation problem for {S}obolev maps between two manifolds }, Pages = { 47-113 }, Note = { Th\`ese, Orsay }, Year = { 1989 } } @Article{ Bet90, Author = { F. Bethuel }, Title = { {A} characterization of maps in {${H}^1({B}^3, {S}^2)$} which can be approximated by smooth maps }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 7 }, Pages = { 269-286 }, Year = { 1990 } } @Unpublished{ Bet90A, Author = { F. Bethuel }, Title = { {E}nergies relax\'ees pour applications harmoniques }, Note = { S\'em. Eq. D\'er. Part. 1989/90. Ecole Polytech. }, Year = { 1990 } } @Article{ Bet92, Author = { F. Bethuel }, Title = { {U}n r{\'e}sultat de r{\'e}gularit{\'e} pour les solutions de l'{\'e}quation des surfaces {\`a} courbure moyenne prescrite }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 314 }, Pages = { 1003-1007 }, Year = { 1992 } } @Article{ Bet93, Author = { F. Bethuel }, Title = { {O}n the singular set of stationary harmonic maps }, Journal = { Manuscripta Math. }, Volume = { 78 }, Pages = { 417-443 }, Year = { 1993 } } @Article{ Bet93A, Author = { F. Bethuel }, Title = { {W}eak limits of {P}alais--{S}male sequences for a class of critical functionals }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 267-310 }, Year = { 1993 } } @Article{ BetBre90, Author = { F. Bethuel and H. Brezis }, Title = { {M}inimisation de {$\int \vert\nabla (u-(x/\vert x\vert))\vert^2$} et divers ph{\'e}nom{\`e}nes de gap }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 310 }, Pages = { 859-864 }, Year = { 1990 } } @Article{ BetBre90A, Author = { F. Bethuel and H. Brezis }, Title = { {R}\'egularit\'e des minima de probl\`emes relax\'es pour les applications harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 310 }, Pages = { 827-829 }, Year = { 1990 } } @Article{ BetBre91, Author = { F. Bethuel and H. Brezis }, Title = { {R}egularity of minimizers of relaxed problems for harmonic maps }, Journal = { J. Funct.\ Anal. }, Volume = { 101 }, Pages = { 145-161 }, Year = { 1991 } } @Article{ BetBreCol92, Author = { F. Bethuel and H. Brezis and B.D. Coleman and F. H{\'e}lein }, Title = { {B}ifurcation analysis of minimizing harmonic maps describing the equilibrium of nematic phases between cylinders }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 118 }, Pages = { 149-168 }, Year = { 1992 } } @Article{ BetBreCor86, Author = { F. Bethuel and H. Brezis and J.-M. Coron }, Title = { {H}armonic maps with defects }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 107 }, Pages = { 619-705 }, Year = { 1986 } } @Incollection{ BetBreCor90, Author = { F. Bethuel and H. Brezis and J.-M. Coron }, Title = { {R}elaxed energies for harmonic maps }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 37-52 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Article{ BetBreHel92, Author = { F. Bethuel and H. Brezis and F. H{\'e}lein }, Title = { {L}imite singuli{\`e}re pour la minimization de fonctionelles du type {G}inzburg-{L}andau }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 314 }, Pages = { 891-895 }, Year = { 1992 } } @Article{ BetBreHel93, Author = { F. Bethuel and H. Brezis and F. H{\'e}lein }, Title = { {A}symptotics for the minimization of a {G}inzburg-{L}andau functional }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 123-148 }, Year = { 1993 } } @Book{ BetBreHel94, Author = { F. Bethuel and H. Brezis and F. H{\'e}lein }, Title = { {G}inzburg-{L}andau vortices }, Publisher = { Birkha\"user }, Address = { Boston }, Volume = { 13 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1994 } } @Incollection{ BetCorDem91, Author = { F. Bethuel and J.-M. Coron and F. Demengel and F. H{\'e}lein }, Title = { {A} cohomological criterion for density of smooth maps in {S}obolev spaces between two manifolds }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Incollection{ BetCorGhi92, Author = { F. Bethuel and J.-M. Coron and J.-M. Ghidaglia and A. Soyeur }, Title = { {H}eat flows and relaxed energies for harmonic maps }, Booktitle = { {N}onlinear diffusion equations and their equilibrium states, 3 }, Editor = { N.G. Lloyd and W.M. Ni and L.A. Peletier and J. Serrin }, Volume = { 7 }, Pages = { 99-109 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1992 } } @Misc{ BetGhi, Author = { F. Bethuel and J.M. Ghidaglia }, Title = { {A} regularity theorem for solutions to the equation of surfaces of prescribed mean curvature } } @Article{ BetGhiA, Author = { F. Bethuel and J.M. Ghidaglia }, Title = { {S}ome applications of the coarea formula to partial differential equations }, Journal = { Geo in P.D.E. } } @Article{ BetGhi93, Author = { F. Bethuel and J.M. Ghidaglia }, Title = { {I}mproved regularity of solutions to elliptic equations involving {J}acobian and applications }, Journal = { J. Math.\ Pures Appl. }, Volume = { 72 }, Pages = { 441-473 }, Year = { 1993 } } @Misc{ BetRey, Author = { F. Bethuel and O. Rey }, Title = { {L}arge solutions for the equation of surfaces of prescribed mean curvature } } @Article{ BetRey94, Author = { F. Bethuel and O. Rey }, Title = { {M}ultiple solutions to the {P}lateau problem for non constant mean curvature }, Journal = { Duke Math.\ J. }, Volume = { 73 }, Pages = { 593-646 }, Year = { 1994 } } @Article{ BetZhe86, Author = { F. Bethuel and X. Zheng }, Title = { {S}ur la densit\'e des fonctions r\'eguli\`eres entre deux vari\'et\'es dans des espaces de {S}obolev }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 303 }, Pages = { 447-449 }, Year = { 1986 } } @Article{ BetZhe88, Author = { F. Bethuel and X. Zheng }, Title = { {D}ensity of smooth functions between two manifolds in {S}obolev spaces }, Journal = { J. Funct.\ Anal. }, Volume = { 80 }, Pages = { 60-75 }, Year = { 1988 } } @Article{ BeuVan88, Author = { P. Beuken and L. Vanhecke }, Title = { {H}armonic reflections on {S}asakian manifolds }, Journal = { Math.\ J. Okayama Univ. }, Volume = { 30 }, Pages = { 187-197 }, Year = { 1988 } } @Article{ BeuVan92, Author = { P. Beuken and L. Vanhecke }, Title = { {R}otations and harmonicity in contact geometry }, Journal = { Rend.\ Mat.\ Appl. }, Volume = { 12 }, Pages = { 127-141 }, Year = { 1992 } } @Article{ BisONe69, Author = { R.L. Bishop and B. O'Neill }, Title = { {M}anifolds of negative curvature }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 145 }, Pages = { 1-49 }, Year = { 1969 } } @Unpublished{ Biz94, Author = { P. Biz{\'o}n }, Title = { {H}armonic maps between three-spheres }, Note = { Preprint }, Year = { 1994 } } @Article{ BizChm97, Author = { P. Biz{\'o}n and T. Chmaj }, Title = { {H}armonic maps between spheres }, Journal = { Proc.\ Roy.\ Soc.\ London Ser.\ A }, Volume = { 453 }, Pages = { 403--415 }, Year = { 1997 } } @Book{ Bla91, Author = { M.J. Black }, Title = { {H}armonic maps into homogeneous spaces }, Publisher = { Longman }, Address = { Harlow }, Volume = { 255 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1991 } } @Misc{ Bla, Author = { D.E. Blair }, Title = { {C}urvature functionals on subspaces of metrics } } @Article{ Bla83, Author = { D.E. Blair }, Title = { {O}n the set of metrics associated to a symplectic or contact form }, Journal = { Bull.\ Inst.\ Math.\ Acad.\ Sinica }, Volume = { 11 }, Pages = { 297-308 }, Year = { 1983 } } @Incollection{ Bla85, Author = { D.E. Blair }, Title = { {C}ritical points of functions of the curvature on spaces of associated metrics }, Booktitle = { {D}ifferential {G}eometry }, Editor = { L.A. Cordero }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 131 }, Pages = { 1-6 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Incollection{ Bla91A, Author = { D.E. Blair }, Title = { {T}he ``total scalar curvature'' as a symplectic invariant }, Booktitle = { {P}roc. 3d {C}ongress of {G}eometry, {T}hessaloniki }, Pages = { 79-83 }, Year = { 1991 } } @Incollection{ BlaIan86, Author = { D.E. Blair and S. Ianus }, Title = { {C}ritical associated metrics on symplectic manifolds }, Booktitle = { {N}onlinear problems in geometry }, Editor = { D. DeTurck }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 51 }, Pages = { 23-29 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Article{ BlaPer92, Author = { D.E. Blair and D. Perrone }, Title = { {A} variational characterization of contact metric manifold with vanishing torsion }, Journal = { Canad.\ Math.\ Bull. }, Volume = { 35 }, Pages = { 455-462 }, Year = { 1992 } } @Article{ Ble79, Author = { D.D. Bleecker }, Title = { {C}ritical mappings of {R}iemannian manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 254 }, Pages = { 319-338 }, Year = { 1979 } } @Article{ Ble79A, Author = { D.D. Bleecker }, Title = { {C}ritical {R}iemannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 14 }, Pages = { 599-608 }, Year = { 1979 } } @Article{ Ble85, Author = { D.D. Bleecker }, Title = { {S}ymmetry breakdown in principal bundles and physical applications }, Journal = { Phys.\ D }, Volume = { 17 }, Pages = { 257-278 }, Year = { 1985 } } @Misc{ Bob, Author = { A.I. Bobenko }, Title = { {F}inite-gap constant mean curvature tori in {${\bf {R}}^3$} and {${S}^3$} } } @Article{ Bob90, Author = { A.I. Bobenko }, Title = { {I}ntegrable surfaces }, Journal = { Funktsional.\ Anal.\ i Prilozhen }, Volume = { 24 }, Pages = { 68-69 }, Year = { 1990 } } @Article{ Bob91, Author = { A.I. Bobenko }, Title = { {A}ll constant mean curvature tori in {${\bf {R}}^3, {S}^3, {H}^3$} in terms of theta-functions }, Journal = { Math.\ Ann. }, Volume = { 290 }, Pages = { 209-245 }, Year = { 1991 } } @Article{ Bob91A, Author = { A.I. Bobenko }, Title = { {C}onstant mean curvature surfaces and integrable equations }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 46 }, Pages = { 3-42 }, Year = { 1991 } } @Unpublished{ BobEitKit95, Author = { A.I. Bobenko and U. Eitner and A. Kitaev }, Title = { {H}armonic inverse mean curvature surfaces and {P}ainlev\'e equations }, Note = { SFB 288 preprint }, Year = { 1995 } } @Article{ BobIts95, Author = { A.I. Bobenko and A. Its }, Title = { {T}he {P}ainlev{\'e} {I}{I}{I} equation and the {I}wasawa decomposition }, Journal = { Manuscripta Math. }, Volume = { 87 }, Pages = { 369-377 }, Year = { 1995 } } @Article{ BobPin96, Author = { A.I. Bobenko and U. Pinkall }, Title = { {D}iscrete surfaces with constant negative {G}aussian curvature and the {H}irota equation }, Journal = { J. Differential Geom. }, Volume = { 43 }, Pages = { 527-611 }, Year = { 1996 } } @Article{ Boc40, Author = { S. Bochner }, Title = { {H}armonic surfaces in {R}iemann metric }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 47 }, Pages = { 146-154 }, Year = { 1940 } } @Article{ Boc43, Author = { S. Bochner }, Title = { {A}nalytic and meromorphic continuation by means of {G}reen's formula }, Journal = { Ann.\ of Math. }, Volume = { 44 }, Pages = { 652-673 }, Year = { 1943 } } @Article{ Boc55, Author = { S. Bochner }, Title = { {C}urvature and {B}etti numbers in real and complex bundles }, Journal = { Rend.\ Sem.\ Mat.\ Univ.\ Politec.\ Torino }, Volume = { 15 }, Pages = { 255-253 }, Year = { 1955 } } @Book{ BocYan53, Author = { S. Bochner and K. Yano }, Title = { {C}urvature and {B}etti numbers }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 32 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1953 } } @Unpublished{ BojIwa83, Author = { B. Bojarski and T. Iwaniec }, Title = { {$p$}-harmonic equation and quasilinear mappings }, Note = { Bonn preprint }, Year = { 1983 } } @Article{ BolJenRig88, Author = { J. Bolton and G. Jensen and M. Rigoli and L.M. Woodward }, Title = { {O}n conformal minimal immersions of {${S}^2$} into {${\bf {C}}{P}^n$} }, Journal = { Math.\ Ann. }, Volume = { 279 }, Pages = { 599-620 }, Year = { 1988 } } @Incollection{ BolOxbVra91, Author = { J. Bolton and W.M. Oxbury and L. Vrancken and L.M. Woodward }, Title = { {M}inimal immersions of {${\bf {R}}{P}^2$} into {${\bf {C}}{P}^n$} }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Editor = { D. Ferus and U. Pinkall and U. Simon and B. Wegner }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1481 }, Pages = { 18-27 }, Series = { Lecture Notes in Math. }, Year = { 1991 } } @Article{ BolPedWoo95, Author = { J. Bolton and F. Pedit and L.M. Woodward }, Title = { {M}inimal surfaces and the affine {T}oda field model }, Journal = { J. Reine Angew.\ Math. }, Volume = { 459 }, Pages = { 119-150 }, Year = { 1995 } } @Incollection{ BolVraWoo91, Author = { J. Bolton and L. Vrancken and L.M. Woodward }, Title = { {M}inimal immersions of {${S}^2$} and {${\bf {R}}{P}^2$} into {${\bf {C}}{P}^n$} with few higher order singularities }, Booktitle = { {G}eometry and topology of submanifolds {I}{I}{I} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 49-57 }, Year = { 1991 } } @Incollection{ BolVraWoo91A, Author = { J. Bolton and L. Vrancken and L.M. Woodward }, Title = { {M}inimal immersions of surfaces into the nearly {K}{\"a}hler {$6$}-sphere }, Booktitle = { {G}eometry and topology of submanifolds {I}{I}{I} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 58-63 }, Year = { 1991 } } @Article{ BolVraWoo92, Author = { J. Bolton and L. Vrancken and L.M. Woodward }, Title = { {M}inimal immersions of {${S}^2$} and {${\bf {R}}{P}^2$} into {${\bf {C}}{P}^n$} with few higher order singularities }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 111 }, Pages = { 93-101 }, Year = { 1992 } } @Article{ BolVraWoo94, Author = { J. Bolton and L. Vrancken and L.M. Woodward }, Title = { {O}n almost complex curves in the nearly {K}\"ahler {$6$}-sphere }, Journal = { Quart.\ J. Math.\ Oxford }, Volume = { 45 }, Pages = { 407-427 }, Year = { 1994 } } @Incollection{ BolWilWoo85, Author = { J. Bolton and T.J. Willmore and L.M. Woodward }, Title = { {I}mmersions of surfaces into space forms }, Booktitle = { {G}lobal differential geometry and global analysis 1984 }, Editor = { D. Ferus and R.B. Gardner and S. Helgason and U. Simon }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1156 }, Pages = { 46-58 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Article{ BolWoo88, Author = { J. Bolton and L.M. Woodward }, Title = { {O}n immersions of surfaces into space forms }, Journal = { Soochow J. Math. }, Volume = { 14 }, Pages = { 11-31 }, Year = { 1988 } } @Article{ BolWoo88A, Author = { J. Bolton and L.M. Woodward }, Title = { {O}n the {S}imon conjecture for minimal immersions with {${S}^1$}-symmetry }, Journal = { Math.\ Z. }, Volume = { 200 }, Pages = { 111-121 }, Year = { 1988 } } @Incollection{ BolWoo89, Author = { J. Bolton and L.M. Woodward }, Title = { {T}he {R}iemannian geometry of minimal immersions of {${S}^2$} into {${\bf {C}}{P}^n$} }, Booktitle = { {G}eometry and topology of submanifolds }, Editor = { J.M. Morvan and L. Verstraelen }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 13-28 }, Year = { 1989 } } @Incollection{ BolWoo90, Author = { J. Bolton and L.M. Woodward }, Title = { {T}he {S}imon conjecture and minimal immersions with {${S}^1$}-symmetry }, Booktitle = { {G}eometry and topology of submanifolds {I}{I} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 20-31 }, Year = { 1990 } } @Incollection{ BolWoo91, Author = { J. Bolton and L.M. Woodward }, Title = { {C}ongruence of minimal surfaces in {${\bf {C}}{P}^n$} }, Booktitle = { {G}eometry and topology of submanifolds {I}{I}{I} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 64-72 }, Year = { 1991 } } @Article{ BolWoo92, Author = { J. Bolton and L.M. Woodward }, Title = { {C}ongruence theorems for harmonic maps of surfaces into {${\bf {C}}{P}^n$} and {${S}^n $} }, Journal = { J. London Math.\ Soc. }, Volume = { 45 }, Pages = { 363-376 }, Year = { 1992 } } @Article{ BolWoo92A, Author = { J. Bolton and L.M. Woodward }, Title = { {M}inimal surfaces in {${\bf {C}}{P}^n$} with constant curvature and {K}{\"a}hler angle }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 112 }, Pages = { 287-296 }, Year = { 1992 } } @Incollection{ BolWoo92B, Author = { J. Bolton and L.M. Woodward }, Title = { {M}oduli spaces of harmonic {$2$}-spheres }, Booktitle = { {G}eometry and {T}opology of {S}ubmanifolds, {I}{V} }, Editor = { F. Dillen and L. Verstraelen }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 143-151 }, Year = { 1992 } } @Incollection{ BolWoo93, Author = { J. Bolton and L.M. Woodward }, Title = { {T}he affine {T}oda equations in the geometry of surfaces }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 175-189 }, Year = { 1993 } } @Incollection{ BolWoo93A, Author = { J. Bolton and L.M. Woodward }, Title = { {A}lmost complex curves of constant curvature in the nearly {K}{\"a}hler {$6$}-sphere }, Booktitle = { {G}eometry and {T}opology of {S}ubmanifolds, {V} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 54-67 }, Year = { 1993 } } @Incollection{ BolWoo93B, Author = { J. Bolton and L.M. Woodward }, Title = { {T}he space of harmonic maps of {${S}^2$} into {${S}^{2m}$} }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 165-173 }, Year = { 1993 } } @Incollection{ BolWoo94, Author = { J. Bolton and L.M. Woodward }, Title = { {T}he affine {T}oda equations and miminal surfaces }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 59-82 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ BomDeGGiu69, Author = { E. Bombieri and E. De~Giorgi and E. Giusti }, Title = { {M}inimal cones and the {B}ernstein problem }, Journal = { Invent.\ Math. }, Volume = { 7 }, Pages = { 243-268 }, Year = { 1969 } } @Article{ BooKobWan63, Author = { W.M. Boothby and S. Kobayashi and H.C. Wang }, Title = { {A} note on mappings and automorphisms of almost complex manifolds }, Journal = { Ann.\ of Math. }, Volume = { 77 }, Pages = { 329-334 }, Year = { 1963 } } @Article{ BorGar80, Author = { H.J. Borchers and W.D. Garber }, Title = { {A}nalyticity of solutions of the {${O}({N})$} non-linear {$\sigma$}-model }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 71 }, Pages = { 299-309 }, Year = { 1980 } } @Article{ BorGar80A, Author = { H.J. Borchers and W.D. Garber }, Title = { {L}ocal theory of solutions for the {${O}(2k+1)$} {$\sigma$}-model }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 72 }, Pages = { 77-102 }, Year = { 1980 } } @Incollection{ BorForLaa94, Author = { M. Bordemann and M. Forger and J. Laartz and U. Sch\"aper }, Title = { {$2$}-dimensional nonlinear sigma models: zero curvature and {P}oisson structure }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 175-192 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ Bor63, Author = { A. Borel }, Title = { {C}ompact {C}lifford--{K}lein forms of symmetric spaces }, Journal = { Topology }, Volume = { 2 }, Pages = { 111-122 }, Year = { 1963 } } @Article{ BorNar67, Author = { A. Borel and R. Narasimhan }, Title = { {U}niqueness conditions for certain holomorphic mappings }, Journal = { Invent.\ Math. }, Volume = { 2 }, Pages = { 247-255 }, Year = { 1967 } } @Article{ BorRem62, Author = { A. Borel and R. Remmert }, Title = { \"{U}ber kompakte homogene {K}\"ahlersche {M}annigfaltigkeiten }, Journal = { Math.\ Ann. }, Volume = { 145 }, Pages = { 429-439 }, Year = { 1961/62 } } @Unpublished{ Bor, Author = { A.A. Borisenko }, Title = { {H}armonic morphisms associated to minimal strongly parabolic surfaces in {E}uclidean space }, Note = { Preprint } } @Incollection{ Bor93, Author = { A.A. Borisenko }, Title = { {R}uled special {L}agrangian surfaces }, Booktitle = { {M}inimal surfaces }, Editor = { A.T. Fomenko }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 15 }, Pages = { 269-285 }, Series = { Adv.\ Soviet Math. }, Year = { 1993 } } @Incollection{ Bor88, Author = { A.Y. Borisovich }, Title = { {P}lateau operator and bifurcations of two-dimensional minimal surfaces }, Booktitle = { {G}lobal {A}nalysis - {S}tudies and {A}pplications {I}{I}{I} }, Editor = { Y.G. Borisovich and Y.E. Gliklikh }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1334 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Article{ Bor88A, Author = { A.Y. Borisovich }, Title = { {T}he reduction of the problem of bifurcation of minimal surfaces to operator equations and the search for bifurcations of a catenoid, a helicoid and the {S}cherk and {E}nneper surfaces }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 43 }, Number = { 5 }, Pages = { 165-166 }, Year = { 1988 } } @Article{ Bou70, Author = { L. Bouche }, Title = { {C}onnexions riemanniennes fibr\'ees et applications harmoniques }, Journal = { Rend.\ Mat. }, Volume = { 3 }, Pages = { 787-804 }, Year = { 1970 } } @Article{ Bou70A, Author = { L. Bouche }, Title = { {S}ur la d\'efinition des applications harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 270 }, Pages = { 120-122 }, Year = { 1970 } } @Article{ BouHou74, Author = { L. Bouche and J. Houillot }, Title = { {C}omposition de d\'eformations infinit\'esimales harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 278 }, Pages = { 783-785 }, Year = { 1974 } } @Article{ BouWol90, Author = { J. Bourgain and T. Wolff }, Title = { {A} remark on gradients of harmonic functions in dimension {$\ge 3$} }, Journal = { Colloq.\ Math. }, Pages = { 253-260 }, Year = { 1990 } } @Incollection{ Bou84, Author = { J.-P. Bourguignon }, Title = { {M}etrics with harmonic curvature }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 18-26 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Incollection{ Bou85, Author = { J.-P. Bourguignon }, Title = { {V}ariational problems of differential geometry in physics }, Booktitle = { {A}tti del {C}onvegno--{S}tudio {S}ulla {G}eometria della {V}ariet\`a {D}ifferenziabili }, Editor = { I. Cattaneo~Gasparini }, Publisher = { Pitagora }, Address = { Bologna }, Pages = { 41-95 }, Year = { 1985 } } @Incollection{ Bou87, Author = { J.-P. Bourguignon }, Title = { {S}ph\`eres minimales ({D}'apr\`es {J}. {S}acks et {K}. {U}hlenbeck) }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 245-254 }, Series = { Ast\'erisque }, Year = { 1987 } } @Incollection{ BouLaw87, Author = { J.-P. Bourguignon and H.B. Lawson }, Title = { {F}ormules de variations de l'aire et applications }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 51-71 }, Series = { Ast\'erisque }, Year = { 1987 } } @Article{ BoyMan88, Author = { C.P. Boyer and B.M. Mann }, Title = { {M}onopoles, nonlinear {$\sigma$}-models, and two-fold loop spaces }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 115 }, Pages = { 571-594 }, Year = { 1988 } } @Book{ Bra78, Author = { K. Brakke }, Title = { {T}he motion of a surface by its mean curvature }, Publisher = { Princeton Univ.\ Press }, Year = { 1978 } } @Incollection{ Bre, Author = { H. Brezis }, Title = { {M}etastable harmonic maps }, Booktitle = { {M}etastability and incompletely posed problems }, Publisher = { Springer }, Address = { Berlin }, Volume = { 3 }, Pages = { 33-4 }, Series = { IMA Vol.\ Math.\ Appl. } } @Incollection{ BreA, Author = { H. Brezis }, Title = { {N}ew energies for harmonic maps and liquid crystals }, Booktitle = { {F}unctional analysis and related topics }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1540 }, Pages = { 11-24 }, Series = { Lecture Notes in Math. } } @Incollection{ Bre85, Author = { H. Brezis }, Title = { {L}arge harmonic maps in two dimensions }, Booktitle = { {N}onlinear {V}ariational {P}roblems }, Editor = { A. Marino and L. Modica and S. Spagnolo and M. Degiovanni }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 127 }, Pages = { 33-46 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Incollection{ Bre87, Author = { H. Brezis }, Title = { {L}iquid crystals and {${S}^2$}-valued maps }, Booktitle = { {C}ontributions to nonlinear partial differential equations, volume {I}{I} }, Editor = { J.I. D{\'\i}az and P.-L. Lions }, Publisher = { Longman }, Address = { Harlow }, Volume = { 155 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1987 } } @Incollection{ Bre87A, Author = { H. Brezis }, Title = { {L}iquid crystals and energy estimates for {${S}^2$}-valued maps }, Booktitle = { {T}heory and applications of liquid crystals }, Editor = { J.L. Ericksen and D. Kinderlehrer }, Publisher = { Springer }, Address = { Berlin }, Volume = { 5 }, Pages = { 31-52 }, Series = { IMA Vol.\ Math.\ Appl. }, Year = { 1987 } } @Incollection{ Bre88, Author = { H. Brezis }, Title = { {P}oints critiques dans les probl\`emes variationnels sans compacit\'e }, Booktitle = { {S}\'em. {B}ourbaki 1987/88 }, Volume = { 161/2 }, Series = { Ast\'erisque }, Year = { 1988 } } @Incollection{ Bre89, Author = { H. Brezis }, Title = { {${S}^k$}-valued maps with singularities }, Booktitle = { {T}opics in calculus of variations }, Editor = { M. Giaquinta }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1365 }, Pages = { 1-30 }, Series = { Lecture Notes in Math. }, Year = { 1989 } } @Article{ BreCor82, Author = { H. Brezis and J.-M. Coron }, Title = { {S}ur la conjecture de {R}ellich pour les surfaces \`a courbure moyenne prescrite }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 295 }, Pages = { 615-618 }, Year = { 1982 } } @Article{ BreCor83, Author = { H. Brezis and J.-M. Coron }, Title = { {L}arge solutions for harmonic maps in two dimensions }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 92 }, Pages = { 203-215 }, Year = { 1983 } } @Article{ BreCor84, Author = { H. Brezis and J.-M. Coron }, Title = { {C}onvergence de solutions de {${H}$}-syst\`emes et applications aux surfaces \`a courbure moyenne constante }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 298 }, Pages = { 389-392 }, Year = { 1984 } } @Article{ BreCor84A, Author = { H. Brezis and J.-M. Coron }, Title = { {M}ultiple solutions of {${H}$}-systems and {R}ellich's conjecture }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 37 }, Pages = { 149-187 }, Year = { 1984 } } @Article{ BreCor85, Author = { H. Brezis and J.-M. Coron }, Title = { {C}onvergence of solutions of {${H}$}-systems or how to blow bubbles }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 89 }, Pages = { 21-56 }, Year = { 1985 } } @Article{ BreCorLie86, Author = { H. Brezis and J.-M. Coron and E.H. Lieb }, Title = { {E}stimations d'\'energie pour les applications de {${\bf {R}}^3$} \`a valeurs dans {${S}^2$} }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 303 }, Pages = { 207-210 }, Year = { 1986 } } @Article{ BreCorLie86A, Author = { H. Brezis and J.-M. Coron and E.H. Lieb }, Title = { {H}armonic maps with defects }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 107 }, Pages = { 649-705 }, Year = { 1986 } } @Incollection{ BreKic89, Author = { H. Brezis and S. Kichenassamy }, Title = { {E}nergy estimates for surface-valued maps with prescribed singularities }, Booktitle = { {N}onlinear {V}ariational {P}roblems {I}{I} }, Editor = { A. Marino and M.K. Murthy }, Publisher = { Longman }, Address = { Harlow }, Volume = { 193 }, Pages = { 92-98 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1989 } } @Article{ BriFla76, Author = { D. Brill and F. Flaherty }, Title = { {I}solated maximal surfaces in spacetime }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 50 }, Pages = { 157-165 }, Year = { 1976 } } @Article{ BroPar94, Author = { R. Brockett and F. Park }, Title = { {K}inematic dexterity of robotic mechanisms }, Journal = { Internat.\ J. Robotics Research }, Volume = { 13 }, Pages = { 1-15 }, Year = { 1994 } } @Article{ Bro78, Author = { R. Brody }, Title = { {C}ompact manifolds and hyperbolicity }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 235 }, Pages = { 213-219 }, Year = { 1978 } } @Article{ Bry, Author = { R. Bryant }, Title = { {S}urfaces of mean curvature one in hyperbolic space }, Journal = { Trans.\ Amer.\ Math.\ Soc. } } @Article{ Bry82, Author = { R. Bryant }, Title = { {C}onformal and minimal immersions of compact surfaces into the {$4$}-sphere }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 455-473 }, Year = { 1982 } } @Article{ Bry82A, Author = { R. Bryant }, Title = { {S}ubmanifolds and special structures on the octonians }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 185-232 }, Year = { 1982 } } @Article{ Bry84, Author = { R. Bryant }, Title = { {A} duality theorem for {W}illmore surfaces }, Journal = { J. Differential Geom. }, Volume = { 20 }, Pages = { 23-53 }, Year = { 1984 } } @Article{ Bry85, Author = { R. Bryant }, Title = { {L}ie groups and twistor spaces }, Journal = { Duke Math.\ J. }, Volume = { 52 }, Pages = { 223-261 }, Year = { 1985 } } @Article{ Bry85A, Author = { R. Bryant }, Title = { {M}inimal surfaces of constant curvature in {${S}^n$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 290 }, Pages = { 259-271 }, Year = { 1985 } } @Incollection{ Bry88, Author = { R. Bryant }, Title = { {S}urfaces in conformal geometry }, Booktitle = { {T}he mathematical heritage of {H}ermann {W}eyl }, Editor = { R.O. Wells }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 48 }, Pages = { 227-240 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1988 } } @Unpublished{ BryA, Author = { R.L. Bryant }, Title = { {H}armonic morphisms with fibers of dimension one }, Note = { preprint } } @Incollection{ BryB, Author = { R.L. Bryant }, Title = { {M}inimal {L}agrangian submanifolds of {K}{\"a}hler--{E}instein manifolds }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations }, Editor = { C.H. Gu and M. Berger and R. Bryant }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1255 }, Pages = { 1-12 }, Series = { Lecture Notes in Math. } } @Unpublished{ Bry94, Author = { R.L. Bryant }, Title = { {O}n extremals with prescribed {L}agrangian densities }, Note = { Preprint }, Year = { 1994 } } @Article{ BudDabFur, Author = { P. Budinich and L. Dabrowski and P. Furlan }, Title = { {M}inimal surfaces and strings from spinors a realization of the {C}artan programme }, Journal = { Nuovo Cimento A (11) }, Volume = { 96 }, Pages = { 194-211 } } @Article{ BudRig, Author = { P. Budinich and M. Rigoli }, Title = { {C}artan spinors, minimal surfaces and strings }, Journal = { Nuovo Cimento B }, Volume = { 102 }, Pages = { 609-647 } } @Article{ BueVan88, Author = { P. Bueken and L. Vanhecke }, Title = { {H}armonic reflections on {S}asakian manifolds }, Journal = { Math.\ J. Okayama Univ. }, Volume = { 30 }, Pages = { 187-197 }, Year = { 1988 } } @Article{ BueVan92, Author = { P. Bueken and L. Vanhecke }, Title = { {R}otations and harmonicity in contact geometry }, Journal = { Rend.\ Mat. }, Volume = { 12 }, Pages = { 127-141 }, Year = { 1992 } } @Article{ Bun87, Author = { G. Bunting }, Title = { {P}roof of the uniqueness conjecture for black holes }, Journal = { Ast{\'e}risque }, Volume = { 155 }, Pages = { 321-347 }, Year = { 1987 } } @Article{ BurHaa95, Author = { O. Burlet and F. Haab }, Title = { {U}n th{\'e}or{\`e}me de rigidit{\'e} pour les surfaces minimales to {${\bf {E}}^3$} }, Journal = { Enseign.\ Math. }, Volume = { (2) 41 }, Pages = { 155-178 }, Year = { 1995 } } @Misc{ Bur, Author = { D. Burns }, Title = { {J}acobi fields on complex cones } } @Incollection{ Bur82, Author = { D. Burns }, Title = { {H}armonic maps from {${\bf {C}}{P}^1$} to {${\bf {C}}{P}^n$} }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 48-56 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ BurGarRui79, Author = { D. Burns and W.D. Garber and S.N.M. Ruijsenaars and E. Seiler }, Title = { {O}n finite action solutions of the nonlinear {$\sigma$}-model }, Journal = { Ann.\ Physics }, Volume = { 119 }, Pages = { 305-325 }, Year = { 1979 } } @Article{ Bur85, Author = { K. Burns }, Title = { {C}onvex supporting domains on surfaces }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 17 }, Pages = { 271-274 }, Year = { 1985 } } @Article{ Bur84, Author = { F.E. Burstall }, Title = { {H}armonic maps of finite energy from non-compact manifolds }, Journal = { J. London Math.\ Soc. }, Volume = { 30 }, Pages = { 361-370 }, Year = { 1984 } } @Unpublished{ Bur84A, Author = { F.E. Burstall }, Title = { {N}on-linear functional analysis and harmonic maps }, Note = { Warwick Ph.D Thesis }, Year = { 1984 } } @Incollection{ Bur85A, Author = { F.E. Burstall }, Title = { {T}wistor fibrations of flag manifolds and harmonic maps of a {$2$}-sphere into a {G}rassmannian }, Booktitle = { {D}ifferential {G}eometry }, Editor = { L.A. Cordero }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 131 }, Pages = { 7-16 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Article{ Bur86, Author = { F.E. Burstall }, Title = { {A} twistor description of harmonic maps of a {$2$}-sphere into a {G}rassmannian }, Journal = { Math.\ Ann. }, Volume = { 274 }, Pages = { 61-74 }, Year = { 1986 } } @Incollection{ Bur87, Author = { F.E. Burstall }, Title = { {T}wistor methods for harmonic maps }, Booktitle = { {D}ifferential {G}eometry }, Editor = { V.L. Hansen }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1263 }, Pages = { 55-96 }, Series = { Lecture Notes in Math. }, Year = { 1987 } } @Incollection{ Bur88, Author = { F.E. Burstall }, Title = { {R}ecent developments in twistor methods for harmonic maps }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 158-176 }, Year = { 1988 } } @Incollection{ Bur90, Author = { F.E. Burstall }, Title = { {M}inimal surfaces in quaternionic symmetric spaces }, Booktitle = { {G}eometry of {L}ow-{D}imensional {M}anifolds, 1 }, Editor = { S.K. Donaldson and C.B. Thomas }, Publisher = { C.U.P. }, Address = { Cambridge }, Volume = { 150 }, Pages = { 231-235 }, Series = { London Math.\ Soc.\ Lecture Note Ser. }, Year = { 1990 } } @Incollection{ Bur90A, Author = { F.E. Burstall }, Title = { {R}iemannian twistor spaces and holonomy groups }, Booktitle = { {T}wistors in mathematics and physics }, Editor = { T.N. Bailey and R.J. Baston }, Publisher = { C.U.P. }, Address = { Cambridge }, Volume = { 156 }, Pages = { 53-70 }, Series = { London Math.\ Soc.\ Lecture Note Ser. }, Year = { 1990 } } @Incollection{ Bur91, Author = { F.E. Burstall }, Title = { {H}armonic tori in {L}ie groups }, Booktitle = { {G}eometry and topology of submanifolds,~{I}{I}{I} }, Editor = { L. Verstraelen and A. West }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 73-80 }, Year = { 1991 } } @Article{ Bur92, Author = { F.E. Burstall }, Title = { {H}armonic maps and soliton theory }, Journal = { Mat.\ Contemp. }, Volume = { 2 }, Pages = { 1-18 }, Year = { 1992 } } @Article{ Bur95, Author = { F.E. Burstall }, Title = { {H}armonic tori in spheres and complex projective spaces }, Journal = { J. Reine Angew.\ Math. }, Volume = { 469 }, Pages = { 149-177 }, Year = { 1995 } } @Article{ BurFerPed93, Author = { F.E. Burstall and D. Ferus and F. Pedit and U. Pinkall }, Title = { {H}armonic tori in symmetric spaces and commuting {H}amiltonian systems on loop algebras }, Journal = { Ann.\ of Math. }, Volume = { 138 }, Pages = { 173-212 }, Year = { 1993 } } @Article{ BurGraska93, Author = { F.E. Burstall and G. Grantcharov and O. Mu{\v s}karov and J. Rawnsley }, Title = { {H}ermitian structures on {H}ermitian symmetric spaces }, Journal = { J. Geom.\ Phys. }, Volume = { 10 }, Pages = { 245-249 }, Year = { 1993 } } @Unpublished{ BurGue96, Author = { F.E. Burstall and M.A. Guest }, Title = { {H}armonic two-spheres in compact symmetric spaces, revisited }, Note = { Preprint }, Year = { 1996 } } @Article{ BurGutRaw93, Author = { F.E. Burstall and S. Gutt and J. Rawnsley }, Title = { {T}wistor spaces for {R}iemmannian symmetric spaces }, Journal = { Math.\ Ann. }, Volume = { 295 }, Pages = { 724-743 }, Year = { 1993 } } @Incollection{ BurPed94, Author = { F.E. Burstall and F. Pedit }, Title = { {H}armonic maps via {A}dler--{K}ostant--{S}ymes theory }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 221-272 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ BurPed95, Author = { F.E. Burstall and F. Pedit }, Title = { {D}ressing orbits of harmonic maps }, Journal = { Duke Math.\ J. }, Volume = { 80 }, Pages = { 353-382 }, Year = { 1995 } } @Article{ BurRaw86, Author = { F.E. Burstall and J. Rawnsley }, Title = { {S}ph\`eres harmoniques dans les groupes de {L}ie compacts et courbes holomorphes dans les espaces homog\`enes }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 302 }, Pages = { 709-712 }, Year = { 1986 } } @Article{ BurRaw87, Author = { F.E. Burstall and J. Rawnsley }, Title = { {S}tability of classical solutions of two dimensional {G}rassmannian models }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 110 }, Pages = { 311-316 }, Year = { 1987 } } @Book{ BurRaw90, Author = { F.E. Burstall and J. Rawnsley }, Title = { {T}wistor theory for {R}iemannian symmetric spaces }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1424 }, Series = { Lecture Notes in Math. }, Year = { 1990 } } @Article{ BurRawSal87, Author = { F.E. Burstall and J. Rawnsley and S.M. Salamon }, Title = { {S}table harmonic {$2$}-spheres in symmetric spaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 16 }, Pages = { 274-278 }, Year = { 1987 } } @Article{ BurSal87, Author = { F.E. Burstall and S.M. Salamon }, Title = { {T}ournaments, flags and harmonic maps }, Journal = { Math.\ Ann. }, Volume = { 277 }, Pages = { 249-265 }, Year = { 1987 } } @Article{ BurWoo86, Author = { F.E. Burstall and J.C. Wood }, Title = { {T}he construction of harmonic maps into complex {G}rassmannians }, Journal = { J. Differential Geom. }, Volume = { 23 }, Pages = { 255-297 }, Year = { 1986 } } @Misc{ BurHerPed, Author = { F. Burstall and U. Hertrich-Jeromin and F. Pedit and U. Pinkall }, Title = { {C}urved flats and isothermic surfaces } } @Article{ Bye70, Author = { W.P. Byers }, Title = { {O}n a theorem of {P}reissmann }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 24 }, Pages = { 50-51 }, Year = { 1970 } } @Misc{ Boh82, Author = { R. B{\"o}hme }, Title = { {N}ew results on the classical problem of {P}lateau on the existence of many solutions }, Number = { 579 }, Series = { S\'eminaire Bourbaki }, Year = { 1981-1982 } } @Article{ BohTro81, Author = { R. B{\"o}hme and A.J. Tromba }, Title = { {T}he index theorem for classical minimal surfaces }, Journal = { Ann.\ of Math. }, Volume = { 113 }, Pages = { 447-499 }, Year = { 1981 } } @Article{ Buc, Author = { J. B{\"u}ch }, Title = { {B}ifurkation von minimalfl{\"a}chen und elementare {K}atastrophen }, Journal = { Manuscripta Math. }, Volume = { 55 }, Pages = { 269-306 } } @Article{ Ber75, Author = { L. B{\'e}rard~Bergery }, Title = { {S}ur certaines fibrations d'espaces homog\`enes {R}iemanniens }, Journal = { Compositio Math. }, Volume = { 30 }, Pages = { 43-61 }, Year = { 1975 } } @Article{ Ber78, Author = { L. B{\'e}rard~Bergery }, Title = { {S}ur la courbure des m\'etriques riemanniennes invariantes des groupes de {L}ie et des espaces homog\`enes }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 11 }, Pages = { 543-576 }, Year = { 1978 } } @Article{ BerBou82, Author = { L. B{\'e}rard~Bergery and J.-P. Bourguignon }, Title = { {L}aplacians and {R}iemannian submersions with totally geodesic fibres }, Journal = { Illinois J. Math. }, Volume = { 26 }, Pages = { 181-200 }, Year = { 1982 } } @Incollection{ BerOch84, Author = { L. B{\'e}rard~Bergery and T. Ochiai }, Title = { {O}n some generalizations of the construction of twistor spaces }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 52-59 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Article{ CadPiuRat95, Author = { R. Caddeo and P. Piu and A. Ratto }, Title = { {${S}{O}(2)$}-invariant minimal and constant mean curvature surfaces in {$3$}-dimensional homogeneous spaces }, Journal = { Manuscripta Math. }, Volume = { 87 }, Pages = { 1-12 }, Year = { 1995 } } @Article{ CafHarSim84, Author = { L. Caffarelli and R. Hardt and L. Simon }, Title = { {M}inimal surfaces with isolated singularities }, Journal = { Manuscripta Math. }, Volume = { 48 }, Pages = { 1-18 }, Year = { 1984 } } @Article{ CahLem88, Author = { M. Cahen and L. Lemaire }, Title = { {A}pplications harmoniques: le succ\`es d'une recherche non planifi\'ee }, Journal = { Acad.\ Roy.\ Belg.\ Bull.\ Cl.\ Sci.\ (5) }, Volume = { 74 }, Pages = { 350-364 }, Year = { 1988 } } @Article{ Cai85, Author = { K.R. Cai }, Title = { {O}n volume-decreasing harmonic maps }, Journal = { J. Math.\ (Wuhan) }, Volume = { 5 }, Pages = { 259-264 }, Year = { 1985 } } @Article{ Cal67, Author = { E. Calabi }, Title = { {M}inimal immersions of surfaces in {E}uclidean spheres }, Journal = { J. Differential Geom. }, Volume = { 1 }, Pages = { 111-125 }, Year = { 1967 } } @Incollection{ Cal67A, Author = { E. Calabi }, Title = { {Q}uelques applications de l'analyse complexe aux surfaces d'aire minima }, Booktitle = { {T}opics in {C}omplex {M}anifolds }, Publisher = { Univ.\ Montr\'eal }, Address = { Montr\'eal }, Pages = { 59-81 }, Year = { 1967 } } @Incollection{ Cal68, Author = { E. Calabi }, Title = { {E}xamples of {B}ernstein problem for some nonlinear equations }, Booktitle = { {G}lobal {A}nalysis, {P}art {I}{I} }, Editor = { S.S. Chern and S. Smale }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 15 }, Pages = { 223-230 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1968 } } @Incollection{ Cal69, Author = { E. Calabi }, Title = { {A}n intrinsic characterization of harmonic one-forms }, Booktitle = { {G}lobal {A}nalysis }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Pages = { 101-117 }, Year = { 1969 } } @Misc{ CalGlu, Author = { E. Calabi and H. Gluck }, Title = { {W}hat are the best almost complex structures on the {$6$}-sphere? } } @Article{ CalHofHof88, Author = { M.J. Callahan and D.A. Hoffman and J.T. Hoffman }, Title = { {C}omputer graphics tools for the study of minimal surfaces }, Journal = { Comm.\ ACM }, Volume = { 31 }, Pages = { 648-661 }, Year = { 1988 } } @Article{ CalHofKar93, Author = { M. Callahan and D.A. Hoffman and H. Karcher }, Title = { {A} family of singly periodic minimal surfaces invariant under a screw motion }, Journal = { Experiment.\ Math. }, Volume = { 2 }, Pages = { 157-182 }, Year = { 1993 } } @Misc{ CalHofMee, Author = { M. Callahan and D.A. Hoffman and W.H. Meeks }, Title = { {E}mbedded minimal surfaces with four ends } } @Article{ CalHofMee89, Author = { M. Callahan and D.A. Hoffman and W.H. Meeks }, Title = { {E}mbedded minimal surfaces with an infinite number of ends }, Journal = { Invent.\ Math. }, Volume = { 96 }, Pages = { 459-505 }, Year = { 1989 } } @Article{ CalHofMee90, Author = { M. Callahan and D.A. Hoffman and W.H. Meeks }, Title = { {T}he structure of singly periodic minimal surfaces }, Journal = { Invent.\ Math. }, Volume = { 99 }, Pages = { 455-481 }, Year = { 1990 } } @Article{ Cam89, Author = { F. Campana }, Title = { {E}spaces de twisteurs dont l'espace des cycles a ses composantes irr{\'e}ductibles compactes }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 308 }, Pages = { 565-568 }, Year = { 1989 } } @Article{ CaoCho86, Author = { H.D. Cao and B. Chow }, Title = { {C}ompact {K}\"ahler manifolds with nonnegative curvature operator }, Journal = { Invent.\ Math. }, Volume = { 83 }, Pages = { 553-556 }, Year = { 1986 } } @Article{ Car92, Author = { G. Carbou }, Title = { {A}pplications harmoniques {\`a} valeurs dans un cercle }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 314 }, Pages = { 359-362 }, Year = { 1992 } } @Article{ Car93, Author = { G. Carbou }, Title = { {R}egularity for a non linear variational problem in dimension two }, Journal = { Manuscripta Math. }, Volume = { 78 }, Pages = { 37-56 }, Year = { 1993 } } @Article{ CarHer91, Author = { J.A. Carlson and L. Hern{\'a}ndez }, Title = { {H}armonic maps from compact {K}\"ahler manifolds to exceptional hyperbolic spaces }, Journal = { J. Geom.\ Anal. }, Volume = { 1 }, Pages = { 339-357 }, Year = { 1991 } } @Article{ CarKasTol89, Author = { J.A. Carlson and A. Kasparian and D. Toledo }, Title = { {V}ariations of {H}odge structure of maximal dimension }, Journal = { Duke Math.\ J. }, Volume = { 58 }, Pages = { 669-694 }, Year = { 1989 } } @Misc{ CarTol, Author = { J.A. Carlson and D. Toledo }, Title = { {Q}uadratic presentations and nilpotent {K}\"ahlergroups } } @Incollection{ CarTol88, Author = { J.A. Carlson and D. Toledo }, Title = { {I}ntegral manifolds, harmonic mappings and the abelian subspace problem }, Booktitle = { {A}lgebra --- {S}ome {C}urrent {T}rends }, Editor = { L.L. Avramov and K.B. Tchakerian }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1352 }, Pages = { 60-74 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Article{ CarTol89, Author = { J.A. Carlson and D. Toledo }, Title = { {H}armonic mappings of {K}\"ahler manifolds to locally symmetric spaces }, Journal = { Inst.\ Hautes \'Etudes Sci.\ Publ.\ Math. }, Volume = { 69 }, Pages = { 173-201 }, Year = { 1989 } } @Article{ CarTol93, Author = { J.A. Carlson and D. Toledo }, Title = { {R}igidity of harmonic maps of maximum rank }, Journal = { J. Geom.\ Anal. }, Volume = { 3 }, Pages = { 99-140 }, Year = { 1993 } } @Article{ Car38, Author = { E. Cartan }, Title = { {F}amilles de surfaces isoparam\'etriques dans les espaces \`a courbure constante }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 17 }, Pages = { 177-191 }, Year = { 1938 } } @Article{ Car39, Author = { E. Cartan }, Title = { {S}ur des familles remarquables d'hypersurfaces isoparam\'etriques dans les espaces sph\'eriques }, Journal = { Math.\ Z. }, Volume = { 45 }, Pages = { 335-367 }, Year = { 1939 } } @Incollection{ Car39A, Author = { E. Cartan }, Title = { {S}ur quelques familles remarquables d'hypersurfaces }, Booktitle = { {C}.{R}. {C}ongr\`es {M}ath. {L}i\`ege }, Pages = { 30-41 }, Year = { 1939 } } @Article{ Car40, Author = { E. Cartan }, Title = { {S}ur des familles d'hypersurfaces isoparam\'etriques des espaces sph\'eriques \`a 5 et \`a 9 dimensions }, Journal = { Univ.\ Nac.\ Tucum\'an Rev.\ Ser.\ A }, Volume = { 1 }, Pages = { 5-22 }, Year = { 1940 } } @Misc{ Car, Author = { B. Carter }, Title = { {T}he {B}unting identity and a generalised {M}azur identity for non-linear elliptic systems including the black hole equilibrium problem and gauge coupled {$\sigma$}-models } } @Article{ CarWes82, Author = { S. Carter and A. West }, Title = { {A} characterization of isoparametric hypersurfaces in spheres }, Journal = { J. London Math.\ Soc. }, Volume = { 26 }, Pages = { 183-192 }, Year = { 1982 } } @Article{ CarWes85, Author = { S. Carter and A. West }, Title = { {G}eneralized {C}artan polynomials }, Journal = { J. London Math.\ Soc. }, Volume = { 32 }, Pages = { 305-316 }, Year = { 1985 } } @Article{ CarWes85A, Author = { S. Carter and A. West }, Title = { {I}soparametric systems and transnormality }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 51 }, Pages = { 520-542 }, Year = { 1985 } } @Article{ CarWes90, Author = { S. Carter and A. West }, Title = { {I}soparametric and totally focal submanifolds }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 60 }, Pages = { 609-624 }, Year = { 1990 } } @Article{ CasUrb93, Author = { I. Castro and F. Urbano }, Title = { {L}agrangian surfaces in the complex {E}uclidean plane with conformal {M}aslov form }, Journal = { T\^ohoku Math.\ J. }, Volume = { 45 }, Pages = { 565-582 }, Year = { 1993 } } @Article{ CasUrb94, Author = { I. Castro and F. Urbano }, Title = { {N}ew examples of minimal {L}agrangian tori in the complex projective plane }, Journal = { Manuscripta Math. }, Volume = { 85 }, Pages = { 265-281 }, Year = { 1994 } } @Unpublished{ CasUrb95, Author = { I. Castro and F. Urbano }, Title = { {O}n twistor harmonic surfaces in the complex projective space }, Note = { Preprint }, Year = { 1995 } } @Article{ CasUrb95A, Author = { I. Castro and F. Urbano }, Title = { {T}wistor holomorphic {L}agrangian surfaces in the complex projective and hyperbolic planes }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 13 }, Pages = { 59-67 }, Year = { 1995 } } @Article{ CatCorRei83, Author = { R. Catenacci and M. Cornalba and C. Reina }, Title = { {O}n the energy spectrum and parameter spaces of classical {${\bf {C}}{P}^n$} models }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 89 }, Pages = { 375-386 }, Year = { 1983 } } @Article{ CatCorRei84, Author = { R. Catenacci and M. Cornalba and C. Reina }, Title = { {C}lassical solutions of {${\bf {C}}{P}^n$} non linear {$\sigma$}-models : {A}n algebraic geometrical description }, Journal = { J. Geom.\ Phys. }, Volume = { 1 }, Pages = { 53-84 }, Year = { 1984 } } @Article{ CatMarRei82, Author = { R. Catenacci and M. Martellini and C. Reina }, Title = { {O}n the classical energy spectrum of {${\bf {C}}{P}^n$} models }, Journal = { Phys.\ Lett. }, Volume = { 115 }, Pages = { 461-462 }, Year = { 1982 } } @Article{ CatRei81, Author = { R. Catenacci and C. Reina }, Title = { {A}lgebraic classification of {${\bf {C}}{P}^n$} instanton solutions }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 5 }, Pages = { 469-473 }, Year = { 1981 } } @Article{ Cat89, Author = { I. Cattaneo~Gasparini }, Title = { {F}orme fondamentali di applicatzioni tra variet{\`a}. {A}pplicazioni di {G}auss generaliaate e problemi di immersione }, Journal = { Note Mat. }, Volume = { 9 Suppl. }, Pages = { 1-16 }, Year = { 1989 } } @Article{ Cat93, Author = { I. Cattaneo~Gasparini }, Title = { {S}ome remarks on the second variation formula for the area }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 11 }, Pages = { 221-235 }, Year = { 1993 } } @Incollection{ CecRya81, Author = { T.E. Cecil and P.J. Ryan }, Title = { {T}ight spherical embeddings }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Editor = { D. Ferus and W. K{\"u}hnel and U. Simon and B. Wegner }, Publisher = { Springer }, Address = { Berlin }, Volume = { 838 }, Pages = { 94-104 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Incollection{ Ceg87, Author = { U. Cegrell }, Title = { {S}ubharmonic functions and minimal surfaces }, Booktitle = { {C}omplex analysis {I}{I} }, Editor = { C.A. Berenstein }, Volume = { 1276 }, Pages = { 60-66 }, Series = { Lecture Notes in Math. }, Year = { 1987 } } @Book{ Cha85, Author = { K.C. Chang }, Title = { {I}nfinite dimensional {M}orse theory and its applications }, Publisher = { Presses de l'Universit{\'e} de Montr{\'e}al }, Address = { Montr{\'e}al }, Volume = { 97 }, Series = { S\'em.\ Math.\ Sup. }, Year = { 1985 } } @Incollection{ Cha86, Author = { K.C. Chang }, Title = { {O}n the mountain pass lemma }, Booktitle = { {E}quadiff 6 }, Editor = { J. Vosmansky and M. Zlamal }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1192 }, Pages = { 203-208 }, Series = { Lecture Notes in Math. }, Year = { 1986 } } @Article{ Cha89, Author = { K.C. Chang }, Title = { {H}eat flow and boundary value problem for harmonic maps }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 6 }, Pages = { 363-395 }, Year = { 1989 } } @Incollection{ Cha90, Author = { K.C. Chang }, Title = { {M}orse theory for harmonic maps }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 431-446 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Book{ Cha93, Author = { K.C. Chang }, Title = { {I}nfinite dimensional {M}orse theory and multiple solution problems }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 6 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1993 } } @Incollection{ ChaDin91, Author = { K.C. Chang and W.Y. Ding }, Title = { {A} result on the global existence of heat flows of harmonic maps from {${D}^2$} into {${S}^2$} }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 37-47 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Article{ ChaDinYe92, Author = { K.C. Chang and W.Y. Ding and R. Ye }, Title = { {F}inite-time blow-up of the heat flow of harmonic maps from surfaces }, Journal = { J. Differential Geom. }, Volume = { 36 }, Pages = { 507-515 }, Year = { 1992 } } @Article{ ChaEel86, Author = { K.C. Chang and J. Eells }, Title = { {U}nstable minimal surface coboundaries }, Journal = { Acta Math.\ Sinica }, Volume = { 2 }, Pages = { 233-247 }, Year = { 1986 } } @Incollection{ ChaEel87, Author = { K.C. Chang and J. Eells }, Title = { {H}armonic maps and minimal surface coboundaries }, Booktitle = { {T}he {L}efschetz centennial conference, {P}art {I}{I}{I}: proceedings on differential equations }, Editor = { A. Verjovsky }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 58.3 }, Pages = { 11-18 }, Series = { Contemp.\ Math. }, Year = { 1987 } } @Article{ Cha93A, Author = { S. Chang }, Title = { {O}n minimal hypersurfaces with constant scalar curvatures in {${S}^4$} }, Journal = { J. Differential Geom. }, Volume = { 37 }, Pages = { 523-534 }, Year = { 1993 } } @Misc{ Cha, Author = { S.P. Chang }, Title = { {O}n polynomial k-forms between spheres } } @Misc{ ChaA, Author = { S.P. Chang }, Title = { {O}n quadratic forms between spheres } } @Misc{ ChaGla, Author = { J. Chargoy-Corona and J.F. Glazebrook }, Title = { {N}il-theta functions and harmonic maps of the {$2$}-torus to {${\bf {C}}{P}^2$} } } @Article{ ChaGla88, Author = { J. Chargoy-Corona and J.F. Glazebrook }, Title = { {N}il-instantons associated with the classical torus {${C}{P}^2$} model }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 15 }, Pages = { 213-217 }, Year = { 1988 } } @Incollection{ Cha87, Author = { B. Charlet }, Title = { {L}e probl\`eme de {B}ernstein sph\'erique }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 221-243 }, Series = { Ast\'erisque }, Year = { 1987 } } @Article{ Cha78, Author = { I. Chavel }, Title = { {O}n {A}. {H}urwitz' method in isoperimetric inequalities }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 71 }, Pages = { 275-279 }, Year = { 1978 } } @Book{ Cha84, Author = { I. Chavel }, Title = { {E}igenvalues in {R}iemannian geometry }, Publisher = { Academic Press }, Address = { New York, San Francisco, London }, Year = { 1984 } } @Article{ Che83, Author = { J. Cheeger }, Title = { {S}pectral geometry of singular {R}iemmanian spaces }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 575-657 }, Year = { 1983 } } @Article{ CheGro72, Author = { J. Cheeger and D. Gromoll }, Title = { {O}n the structure of complete manifolds of nonnegative curvature }, Journal = { Ann.\ of Math. }, Volume = { 96 }, Pages = { 413-443 }, Year = { 1972 } } @Article{ CheMulSch84, Author = { J. Cheeger and W. M{\"u}ller and R. Schrader }, Title = { {O}n the curvature of piecewise flat spaces }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 92 }, Pages = { 405-454 }, Year = { 1984 } } @Article{ Che71, Author = { B.Y. Chen }, Title = { {O}n the total curvature of immersed manifolds, {I} }, Journal = { Amer.\ J. Math. }, Volume = { 93 }, Pages = { 145-162 }, Year = { 1971 } } @Article{ Che71A, Author = { B.Y. Chen }, Title = { {S}ubmanifolds in a {E}uclidean hypersphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 27 }, Pages = { 627-628 }, Year = { 1971 } } @Article{ Che72, Author = { B.Y. Chen }, Title = { {O}n the total curvature of immersed manifolds, {I}{I} }, Journal = { Amer.\ J. Math. }, Volume = { 94 }, Pages = { 799-809 }, Year = { 1972 } } @Book{ Che73, Author = { B.Y. Chen }, Title = { {G}eometry of submanifolds }, Publisher = { M. Dekker }, Year = { 1973 } } @Article{ Che73A, Author = { B.Y. Chen }, Title = { {A}n invariant of conformal mappings }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 40 }, Pages = { 563-564 }, Year = { 1973 } } @Article{ Che73B, Author = { B.Y. Chen }, Title = { {O}n a variational problem in hypersurfaces }, Journal = { J. London Math.\ Soc. }, Volume = { 6 }, Pages = { 321-325 }, Year = { 1973 } } @Article{ Che73C, Author = { B.Y. Chen }, Title = { {O}n the surfaces with parallel mean curvature vector }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 22 }, Pages = { 655-666 }, Year = { 1973 } } @Article{ Che73D, Author = { B.Y. Chen }, Title = { {O}n the total curvature of immersed manifolds, {I}{I}{I} }, Journal = { Amer.\ J. Math. }, Volume = { 95 }, Pages = { 636-642 }, Year = { 1973 } } @Article{ Che74, Author = { B.Y. Chen }, Title = { {S}ome conformal invariants of submanifolds and their applications }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 10 }, Pages = { 380-385 }, Year = { 1974 } } @Incollection{ Che75, Author = { B.Y. Chen }, Title = { {M}ean curvature vector of a submanifold }, Booktitle = { {D}ifferential {G}eometry }, Editor = { S.S. Chern and R. Osserman }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 27 }, Pages = { 119-123 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1975 } } @Article{ Che76, Author = { B.Y. Chen }, Title = { {T}otal mean curvature of immersed surfaces in {${E}^m$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 218 }, Pages = { 333-341 }, Year = { 1976 } } @Book{ Che84, Author = { B.Y. Chen }, Title = { {T}otal mean curvature and submanifolds of finite type }, Publisher = { World Scientific Pub. }, Address = { Singapore }, Year = { 1984 } } @Unpublished{ Che85, Author = { B.Y. Chen }, Title = { {F}inite type manifolds and generalizations }, Note = { Rome notes }, Year = { 1985 } } @Article{ CheHou75, Author = { B.Y. Chen and C.S. Houh }, Title = { {O}n stable submanifolds with parallel mean curvature vector }, Journal = { Quart.\ J. Math.\ Oxford }, Volume = { 26 }, Pages = { 229-236 }, Year = { 1975 } } @Misc{ CheLeuNag, Author = { B.Y. Chen and P.F. Leung and T. Nagano }, Title = { {T}otally geodesic submanifolds of symmetric spaces {I}{I}{I} } } @Article{ CheLud72, Author = { B.Y. Chen and G.D. Ludden }, Title = { {S}urfaces with mean curvature vector parallel in the normal bundle }, Journal = { Nagoya Math.\ J. }, Volume = { 47 }, Pages = { 161-167 }, Year = { 1972 } } @Article{ CheMor91, Author = { B.Y. Chen and J.-M. Morvan }, Title = { {S}ur la stabilit{\'e} des sous-vari{\'e}t{\'e}s minimales isotropes d'une vari{\'e}t{\'e} k{\"a}hl{\'e}rienne }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 312 }, Pages = { 685-688 }, Year = { 1991 } } @Article{ CheMorNor85, Author = { B.Y. Chen and J.M. Morvan and T. Nore }, Title = { {E}nergie, tension et ordre des applications \`a valeurs dans un espace euclidien }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 301 }, Pages = { 123-126 }, Year = { 1985 } } @Article{ CheMorNor86, Author = { B.Y. Chen and J.M. Morvan and T. Nore }, Title = { {E}nergy, tension and finite type maps }, Journal = { Kodai Math.\ J. }, Volume = { 9 }, Pages = { 406-418 }, Year = { 1986 } } @Misc{ CheNag, Author = { B.Y. Chen and T. Nagano }, Title = { {H}armonic immersions and {G}auss maps } } @Article{ CheNag77, Author = { B.Y. Chen and T. Nagano }, Title = { {T}otally geodesic submanifolds of symmetric spaces, {I} }, Journal = { Duke Math.\ J. }, Volume = { 44 }, Pages = { 745-755 }, Year = { 1977 } } @Article{ CheNag78, Author = { B.Y. Chen and T. Nagano }, Title = { {T}otally geodesic submanifolds of symmetric spaces, {I}{I} }, Journal = { Duke Math.\ J. }, Volume = { 45 }, Pages = { 405-425 }, Year = { 1978 } } @Article{ CheNag84, Author = { B.Y. Chen and T. Nagano }, Title = { {H}armonic metrics, harmonic tensors and {G}auss maps }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 36 }, Pages = { 295-313 }, Year = { 1984 } } @Article{ CheVan81, Author = { B.Y. Chen and L. Vanhecke }, Title = { {D}ifferential geometry of geodesic spheres }, Journal = { J. Reine Angew.\ Math. }, Volume = { 325 }, Pages = { 28-67 }, Year = { 1981 } } @Article{ CheVan89, Author = { B.Y. Chen and L. Vanhecke }, Title = { {I}sometric, holomorphic and symplectic reflections }, Journal = { Geom.\ Dedicata }, Volume = { 29 }, Pages = { 259-277 }, Year = { 1989 } } @Article{ CheYam83, Author = { B.Y. Chen and S. Yamaguchi }, Title = { {C}lassification of surfaces with totally geodesic {G}auss image }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 32 }, Pages = { 143-154 }, Year = { 1983 } } @Article{ CheYam84, Author = { B.Y. Chen and S. Yamaguchi }, Title = { {S}ubmanifolds with totally geodesic {G}auss image }, Journal = { Geom.\ Dedicata }, Volume = { 15 }, Pages = { 313-322 }, Year = { 1984 } } @Article{ Che81, Author = { C.C. Chen }, Title = { {T}otal curvature and topological structure of complete minimal surfaces }, Journal = { Chinese J. Math. }, Volume = { 9 }, Pages = { 23-38 }, Year = { 1981 } } @Article{ Che82, Author = { C.C. Chen }, Title = { {O}n the image of the generalized {G}auss map of a complete minimal surface in {${\bf {R}}^4$} }, Journal = { Pacific J. Math. }, Volume = { 102 }, Pages = { 9-14 }, Year = { 1982 } } @Article{ CheGoe83, Author = { C.C. Chen and C.C. Goes }, Title = { {D}egenerate minimal surfaces in {${\bf {R}}^4$} }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 14 }, Pages = { 1-16 }, Year = { 1983 } } @Article{ Che93, Author = { J.H. Chen }, Title = { {C}ompact 2-harmonic hypersurface in {${S}^{n+1}(1)$} }, Journal = { Acta Math.\ Sinica }, Volume = { 36 }, Pages = { 341-347 }, Year = { 1993 } } @Incollection{ Che93A, Author = { J.Y. Chen }, Title = { {S}table harmonic maps into {${S}^2$} }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 431-436 }, Year = { 1993 } } @Article{ Che95, Author = { J.Y. Chen }, Title = { {O}n energy minimizing mappings between and into singular spaces }, Journal = { Duke Math.\ J. }, Volume = { 79 }, Pages = { 77-99 }, Year = { 1995 } } @Article{ Che96, Author = { J.Y. Chen }, Title = { {S}table harmonic maps into the complex projective spaces }, Journal = { J. Differential Geom. }, Volume = { 43 }, Pages = { 42-65 }, Year = { 1996 } } @Article{ CheXin92, Author = { Q. Chen and Y.L. Xin }, Title = { {A} generalized maximum principle and its applications in geometry }, Journal = { Amer.\ J. Math. }, Volume = { 114 }, Pages = { 355-366 }, Year = { 1992 } } @Article{ CheXu, Author = { R. Chen and X.W. Xu }, Title = { {O}n the {$m$}-harmonic representatives of maps between ellipsoids }, Journal = { Internat.\ J. Math. } } @Article{ Che83A, Author = { W.H. Chen }, Title = { {A} class of generalized harmonic mappings }, Journal = { Beijing Daxue Xuebao }, Pages = { 10-21 }, Note = { (Chinese, English summary) }, Year = { 1983 } } @Article{ Che87, Author = { W.H. Chen }, Title = { {T}he geometry of {G}rassmann manifolds as submanifolds }, Journal = { Adv.\ in Math.\ (Beijing) }, Volume = { 16 }, Pages = { 334-335 }, Year = { 1987 } } @Article{ Che88, Author = { W.H. Chen }, Title = { {T}he differential geometry of {G}rassmann manifolds as submanifolds }, Journal = { Acta Math.\ Sinica }, Volume = { 31 }, Pages = { 46-53 }, Note = { (Chinese) }, Year = { 1988 } } @Incollection{ Che93B, Author = { W.H. Chen }, Title = { {I}ndefinite {K}\"ahlerian manifolds and minimal surfaces }, Booktitle = { {D}ifferential {G}eometry ({S}hanghai, 1991) }, Publisher = { World Sci.\ Publishing }, Address = { River Edge, NJ }, Pages = { 7-22 }, Year = { 1993 } } @Misc{ CheZan, Author = { W.H. Chen and A. Zandi }, Title = { {N}otes on the classification theorem of certain harmonic maps } } @Incollection{ Che81A, Author = { X.P. Chen }, Title = { {H}armonic mappings and {G}auss mappings }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei 1981 }, Publisher = { Science Press }, Address = { Beijing }, Pages = { 51-53 }, Year = { 1981 } } @Article{ Che83B, Author = { X.P. Chen }, Title = { {H}armonic mappings and {G}auss mapping }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 4 }, Pages = { 449-456 }, Year = { 1983 } } @Incollection{ Che84A, Author = { X.P. Chen }, Title = { {H}armonic mapping and {G}auss mapping }, Booktitle = { {P}roc. 1981 {S}hanghai--{H}efei {S}ymp. {D}iff. {G}eom. {D}iff. {E}qu. }, Publisher = { Sc.\ Press }, Address = { Beijing }, Pages = { 51-53 }, Year = { 1984 } } @Article{ Che84B, Author = { X.P. Chen }, Title = { {S}ome results on the {G}auss mapping of an immersion and harmonic mappings }, Journal = { J. Math.\ (Wuhan) }, Volume = { 4 }, Pages = { 121-126 }, Year = { 1984 } } @Article{ CheXin, Author = { X.P. Chen and Y.L. Xin }, Title = { {H}ypersurfaces with relatively affine {G}auss map into the sphere }, Journal = { Acta Math.\ Sinica } } @Article{ CheGigGot91, Author = { Y.G. Chen and Y. Giga and S. Goto }, Title = { {U}niqueness and existence of viscosity solutions of generated mean curvature flow equation }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 749-786 }, Year = { 1991 } } @Incollection{ Che, Author = { Y.M. Chen }, Title = { {E}volution problems of harmonic maps in higher dimensions }, Booktitle = { {Q}ualitative aspects and applications of nonlinear evolution equations ({T}rieste, 1990) }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 36-42 } } @Article{ Che89, Author = { Y.M. Chen }, Title = { {T}he weak solutions to the evolution problems of harmonic maps }, Journal = { Math.\ Z. }, Volume = { 201 }, Pages = { 69-74 }, Year = { 1989 } } @Article{ Che91, Author = { Y.M. Chen }, Title = { {D}irichlet problems for heat flows of harmonic maps in higher dimensions }, Journal = { Math.\ Z. }, Volume = { 208 }, Pages = { 557-565 }, Year = { 1991 } } @Article{ CheDin90, Author = { Y.M. Chen and W.Y. Ding }, Title = { {B}low up and global existence for heat flows of harmonic maps }, Journal = { Invent.\ Math. }, Volume = { 99 }, Pages = { 567-578 }, Year = { 1990 } } @Incollection{ CheDin91, Author = { Y.M. Chen and W.Y. Ding }, Title = { {B}low-up analysis for heat flow of harmonic maps }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 49-64 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Misc{ CheGao, Author = { Y.M. Chen and J. Gao }, Title = { {H}armonic maps in three dimensional {M}inkowski space with image near geodesics } } @Article{ CheGao93, Author = { Y.M. Chen and J.M. Gao }, Title = { {A} remark on harmonic maps in three-dimensional {M}inkowski space }, Journal = { C. R. Math.\ Rep.\ Acad.\ Sci.\ Canada }, Volume = { 15 }, Pages = { 79-84 }, Year = { 1993 } } @Article{ CheHon94, Author = { Y.M. Chen and M.C. Hong }, Title = { {H}eat flow of {$p$}-harmonic maps with values into spheres }, Journal = { Math.\ Z. }, Volume = { 215 }, Pages = { 25-35 }, Year = { 1994 } } @Misc{ CheLiLin, Author = { Y.M. Chen and J.Y. Li and F.H. Lin }, Title = { {P}artial regularity for weak heat flows into spheres } } @Misc{ CheLin, Author = { Y.M. Chen and F.H. Lin }, Title = { {E}volution equations with a free boundary condition } } @Article{ CheLin93, Author = { Y.M. Chen and F.H. Lin }, Title = { {E}volution of harmonic maps with {D}irichlet boundary conditions }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 327-346 }, Year = { 1993 } } @Article{ CheLin95, Author = { Y.M. Chen and F.H. Lin }, Title = { {R}emarks on approximate harmonic maps }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 70 }, Pages = { 161-169 }, Year = { 1995 } } @Article{ CheMus89, Author = { Y.M. Chen and R. Musina }, Title = { {L}e flot d'applications harmoniques d'une vari\'et\'e compacte sur une vari\'et\'e \`a bord }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 309 }, Pages = { 499-501 }, Year = { 1989 } } @Article{ CheMus90, Author = { Y.M. Chen and R. Musina }, Title = { {H}armonic mappings into manifolds with boundary }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 17 }, Pages = { 365-392 }, Year = { 1990 } } @Article{ CheStr89, Author = { Y.M. Chen and M. Struwe }, Title = { {E}xistence and partial regularity results for the heat flow for harmonic maps }, Journal = { Math.\ Z. }, Volume = { 201 }, Pages = { 83-103 }, Year = { 1989 } } @Article{ CheHonHun94, Author = { Y. Chen and M.C. Hong and N. Hungerb{\"u}hler }, Title = { {H}eat flow of {$p$}-harmonic maps with values into spheres }, Journal = { Math.\ Z. }, Volume = { 215 }, Pages = { 25-35 }, Year = { 1994 } } @Article{ CheCheKen79, Author = { Z.H. Chen and S.Y. Cheng and L.Q. Keng }, Title = { {O}n the {S}chwarz lemma for complete {K}\"ahler manifolds }, Journal = { Sci.\ Sinica }, Volume = { 22 }, Pages = { 1238-1247 }, Year = { 1979 } } @Article{ CheYan81, Author = { Z.H. Chen and H.C. Yang }, Title = { {A} {S}chwarz lemma for a complete manifold whose {R}icci curvature is bounded from below }, Journal = { Acta Math.\ Sinica }, Volume = { 24 }, Pages = { 945-952 }, Year = { 1981 } } @Article{ CheYan83, Author = { Z.H. Chen and H.C. Yang }, Title = { {E}stimations of decreasing coefficients on {${K}$}-dilatation harmonic maps }, Journal = { Kexue Tongbao }, Volume = { 28 }, Pages = { 879-882 }, Year = { 1983 } } @Incollection{ CheYan84, Author = { Z.H. Chen and H.C. Yang }, Title = { {O}n the {S}chwarz lemma for complete {H}ermitian manifolds }, Booktitle = { {S}everal {C}omplex {V}ariables ({H}angzhou 1981) }, Editor = { J.J. Kohn and Q.K. Lu and R. Remmert and Y.T. Siu }, Publisher = { Birkh\"auser }, Address = { Boston }, Pages = { 99-116 }, Year = { 1984 } } @Article{ CheYan85, Author = { Z.H. Chen and H.C. Yang }, Title = { {A} class of {L}iouville theorems }, Journal = { Acta Math.\ Sinica }, Volume = { 28 }, Pages = { 218-232 }, Year = { 1985 } } @Article{ Che90, Author = { Q.M. Cheng }, Title = { {C}omplete minimal hypersurfaces in {${S}^4(1)$} with constant scalar curvature }, Journal = { Osaka J. Math. }, Volume = { 27 }, Pages = { 885-892 }, Year = { 1990 } } @Article{ Che92, Author = { Q.M. Cheng }, Title = { {C}omplete totally real minimal submanifolds in complex projective space }, Journal = { Mem.\ Fac.\ Sci.\ Kyushu Univ.\ Ser.\ A }, Volume = { 46 }, Pages = { 93-103 }, Year = { 1992 } } @Incollection{ CheWan93, Author = { Q.M. Cheng and Q.R. Wan }, Title = { {H}ypersurfaces of space forms {${M}^4(c)$} with constant mean curvature }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 437-442 }, Year = { 1993 } } @Article{ CheWan89, Author = { Q.M. Cheng and Y.D. Wang }, Title = { {C}omplete {R}iemannian manifold minimally immersed in a unit sphere {${S}^{n+p}(1)$} }, Journal = { Tsukuba J. Math. }, Volume = { 13 }, Pages = { 107-112 }, Year = { 1989 } } @Unpublished{ CheDon, Author = { Q.Y. Cheng and Y.X. Dong }, Title = { {O}n factorization theorems of pluriharmonic maps into the unitary group }, Note = { preprint } } @Article{ CheDon96, Author = { Q.Y. Cheng and Y.X. Dong }, Title = { {S}ome remarks on harmonic morphisms }, Journal = { Chinese Sci.\ Bull. }, Volume = { 41 }, Pages = { 1825-1828 }, Year = { 1996 } } @Article{ Che76A, Author = { S.Y. Cheng }, Title = { {A} characterization of the {$2$}-sphere by eigenfunctions }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 55 }, Pages = { 379-381 }, Year = { 1976 } } @Incollection{ Che80, Author = { S.Y. Cheng }, Title = { {L}iouville theorem for harmonic maps }, Booktitle = { {G}eometry of the {L}aplace {O}perator }, Editor = { R. Osserman and A. Weinstein }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 36 }, Pages = { 147-151 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1980 } } @Article{ Che93C, Author = { S.Y. Cheng }, Title = { {T}he {D}irichlet problem at infinity for non-positively curved manifolds }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 101-102 }, Year = { 1993 } } @Article{ CheLiYau84, Author = { S.Y. Cheng and P. Li and S.T. Yau }, Title = { {H}eat equations on minimal submanifolds and their applications }, Journal = { Amer.\ J. Math. }, Volume = { 106 }, Pages = { 1033-1065 }, Year = { 1984 } } @Article{ CheTamWan96, Author = { S.Y. Cheng and L.F. Tam and T.Y.H. Wan }, Title = { {H}armonic maps with finite total energy }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 124 }, Pages = { 275-284 }, Year = { 1996 } } @Article{ CheTys88, Author = { S.Y. Cheng and J. Tysk }, Title = { {A}n index characterization of the catenoid and index bounds for minimal surfaces in {${R}^4$} }, Journal = { Pacific J. Math. }, Volume = { 134 }, Pages = { 251-??? }, Year = { 1988 } } @Article{ CheYau75, Author = { S.Y. Cheng and S.T. Yau }, Title = { {D}ifferential equations on {R}iemannian manifolds and their geometric applications }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 28 }, Pages = { 333-354 }, Year = { 1975 } } @Article{ CheYau76, Author = { S.Y. Cheng and S.T. Yau }, Title = { {M}aximal space-like hypersurfaces in the {L}orentz--{M}inkowski space }, Journal = { Ann.\ of Math. }, Volume = { 104 }, Pages = { 407-419 }, Year = { 1976 } } @Article{ Che91A, Author = { X. Cheng }, Title = { {E}stimate of the singular set of the evolution problem for harmonic maps }, Journal = { J. Differential Geom. }, Volume = { 34 }, Pages = { 169-174 }, Year = { 1991 } } @Article{ Che60, Author = { S.S. Chern }, Title = { {C}omplex analytic mappings of {R}iemann surfaces, {I} }, Journal = { Amer.\ J. Math. }, Volume = { 82 }, Pages = { 323-337 }, Year = { 1960 } } @Article{ Che61, Author = { S.S. Chern }, Title = { {H}olomorphic mappings of complex manifolds }, Journal = { Enseign.\ Math. }, Volume = { 7 }, Pages = { 179-187 }, Year = { 1961 } } @Incollection{ Che65, Author = { S.S. Chern }, Title = { {M}inimal surfaces in an euclidean space of {${N}$} dimensions }, Booktitle = { {D}ifferential and {C}ombinatorial {T}opology, {S}ymposium in {H}onor of {M}arston {M}orse }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Pages = { 187-198 }, Year = { 1965 } } @Article{ Che65A, Author = { S.S. Chern }, Title = { {O}n the curvature of a piece of hypersurface in {E}uclidean space }, Journal = { Abh.\ Math.\ Sem.\ Univ.\ Hamburg }, Volume = { 29 }, Pages = { 77-91 }, Year = { 1965 } } @Incollection{ Che68, Author = { S.S. Chern }, Title = { {O}n holomorphic mappings of {H}ermitian manifolds of the same dimension }, Booktitle = { {E}ntire {F}unctions and related parts of {A}nalysis }, Editor = { S.S. Chern and L. Ehrenpreis and J. Korevaar and W.H.J. Fuchs and L.A. Rubel }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 11 }, Pages = { 157-170 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1968 } } @Article{ Che69, Author = { S.S. Chern }, Title = { {S}imple proofs of two theorems on minimal surfaces }, Journal = { Enseign.\ Math. }, Volume = { 15 }, Pages = { 53-61 }, Year = { 1969 } } @Incollection{ Che70, Author = { S.S. Chern }, Title = { {O}n minimal spheres in the four-sphere }, Booktitle = { {S}tudies and essays presented to {Y}.{W}. {C}hen, {T}aiwan }, Pages = { 137-150 }, Year = { 1970 } } @Incollection{ Che70A, Author = { S.S. Chern }, Title = { {O}n the minimal immersions of the two-sphere in a space of constant curvature }, Booktitle = { {P}roblems in {A}nalysis, {S}ymposium in honor of {S}olomon {B}ochner }, Publisher = { Princeton Univ.\ Press. }, Address = { Princeton }, Pages = { 27-40 }, Year = { 1970 } } @Article{ CheGol75, Author = { S.S. Chern and S.I. Goldberg }, Title = { {O}n the volume decreasing property of a class of real harmonic mappings }, Journal = { Amer.\ J. Math. }, Volume = { 97 }, Pages = { 133-147 }, Year = { 1975 } } @Article{ CheOss67, Author = { S.S. Chern and R. Osserman }, Title = { {C}omplete minimal surfaces in {E}uclidean {$n$}-space }, Journal = { J. Analyse Math. }, Volume = { 19 }, Pages = { 15-34 }, Year = { 1967 } } @Incollection{ CheOss81, Author = { S.S. Chern and R. Osserman }, Title = { {R}emarks on the {R}iemannian metric of a minimal submanifold }, Booktitle = { {G}eom. {S}ymp. {U}trecht, 1980 }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 894 }, Pages = { 49-90 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Article{ CheWol83, Author = { S.S. Chern and J.G. Wolfson }, Title = { {M}inimal surfaces by moving frames }, Journal = { Amer.\ J. Math. }, Volume = { 105 }, Pages = { 59-83 }, Year = { 1983 } } @Article{ CheWol85, Author = { S.S. Chern and J.G. Wolfson }, Title = { {H}armonic maps of {${S}^2$} into a complex {G}rassmann manifold }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 82 }, Pages = { 2217-2219 }, Year = { 1985 } } @Article{ CheWol87, Author = { S.S. Chern and J.G. Wolfson }, Title = { {H}armonic maps of the two-sphere into a complex {G}rassmann manifold. {I}{I} }, Journal = { Ann.\ of Math. }, Volume = { 125 }, Pages = { 301-335 }, Year = { 1987 } } @Article{ Che94, Author = { L.F. Cheung }, Title = { {T}he non-existence of some noncompact constant mean curvature surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 121 }, Pages = { 1207-1209 }, Year = { 1994 } } @Article{ CheLeu94, Author = { L.F. Cheung and P.F. Leung }, Title = { {S}ome results on stable {$p$}-harmonic maps }, Journal = { Glasgow Math.\ J. }, Volume = { 36 }, Pages = { 77-80 }, Year = { 1994 } } @Article{ CheLeu95, Author = { L.F. Cheung and P.F. Leung }, Title = { {A} remark on convex functions and p-harmonic maps }, Journal = { Geom.\ Dedicata }, Volume = { 56 }, Pages = { 269-270 }, Year = { 1995 } } @Article{ ChiPar92, Author = { D.P. Chi and G.H. Park }, Title = { {W}eak-stability of {$x/\{V}ert x\{V}ert$} and symmetries of liquid crystals }, Journal = { J. Korean Math.\ Soc. }, Volume = { 29 }, Pages = { 251-260 }, Year = { 1992 } } @Unpublished{ ChiFerWu96, Author = { Q.-S. Chi and L. Fernandez and H. Wu }, Title = { {N}ormalized potentials of minimal surfaces in spheres }, Note = { Preprint }, Year = { 1996 } } @Article{ Chi90, Author = { Q.S. Chi }, Title = { {R}igidity of superminimal immersions of compact {R}iemann surfaces into {${\bf {C}}{P}^2$} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 42 }, Pages = { 439-455 }, Year = { 1990 } } @Article{ ChiJenLia95, Author = { Q.S. Chi and G. Jensen and R. Liao }, Title = { {I}soparametric functions and flat minimal tori in {${\bf {C}}{P}^2$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 123 }, Pages = { 2849-2854 }, Year = { 1995 } } @Misc{ ChiMo, Author = { Q.S. Chi and X.K. Mo }, Title = { {T}he moduli space of branched superminimal surfaces of fixed degree, genus and conformal structure in the four-sphere } } @Article{ ChiMo92, Author = { Q.S. Chi and X.K. Mo }, Title = { {R}igidity of superminimal surfaces in complex projective spaces }, Journal = { T\^ohoku Math.\ J. }, Volume = { 42 }, Pages = { 83-101 }, Year = { 1992 } } @Article{ ChiZhe89, Author = { Q.S. Chi and Y. Zheng }, Title = { {R}igidity of pseudo-holomorphic curves of constant curvature in {G}rassmann manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 313 }, Pages = { 393-406 }, Year = { 1989 } } @Misc{ Chi, Author = { Y.J. Chiang }, Title = { {H}armonic maps from {R}iemann surfaces into higher dimensional manifolds } } @Article{ Chi90A, Author = { Y.J. Chiang }, Title = { {H}armonic maps of {${V}$}-manifolds }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 8 }, Pages = { 315-344 }, Year = { 1990 } } @Incollection{ Chi93, Author = { Y.J. Chiang }, Title = { {S}pectral geometry of {${V}$}-manifolds and its application to harmonic maps }, Booktitle = { {D}ifferential {G}eometry: : partial differential equations on manifolds }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { American Math.\ Soc. }, Address = { Providence RI }, Volume = { 54:1 }, Pages = { 93-99 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ ChiRat92, Author = { Y.J. Chiang and A. Ratto }, Title = { {H}armonic maps on spaces with conical singularities }, Journal = { Bull.\ Soc.\ Math.\ France }, Volume = { 120 }, Pages = { 251-262 }, Year = { 1992 } } @Unpublished{ Cho, Author = { J.Y. Choe }, Title = { {T}he isoenergy inequality for a harmonic map }, Note = { preprint } } @Misc{ ChoA, Author = { J.Y. Choe }, Title = { {O}n the analytic reflection of a minimal surface } } @Article{ Cho90, Author = { J.Y. Choe }, Title = { {I}ndex, vision number and stability of complete minimal surfaces }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 109 }, Pages = { 195-212 }, Year = { 1990 } } @Article{ ChoGul, Author = { J.Y. Choe and R. Gulliver }, Title = { {I}soperimetric inequalities on minimal submanifolds of space forms }, Journal = { Invent.\ Math. } } @Article{ Cho75, Author = { M.N. Chofii }, Title = { {S}ur un th\'eor\`eme de {H}ans {L}ewy }, Journal = { Bull.\ Sci.\ Math }, Volume = { 99 }, Pages = { 291-292 }, Year = { 1975 } } @Incollection{ ChoB, Author = { H.I. Choi }, Title = { {D}egenerate harmonic maps and liquid crystal }, Booktitle = { {T}heory and applications of liquid crystals }, Editor = { J.L. Ericksen and D. Kinderlehrer }, Publisher = { Springer }, Address = { Berlin }, Volume = { 5 }, Series = { IMA Vol.\ Math.\ Appl. } } @Article{ Cho82, Author = { H.I. Choi }, Title = { {O}n the {L}iouville theorem for harmonic maps }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 85 }, Pages = { 91-94 }, Year = { 1982 } } @Article{ Cho84, Author = { H.I. Choi }, Title = { {A}symptotic {D}irichlet problems for harmonic functions on {R}iemannian manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 281 }, Pages = { 691-716 }, Year = { 1984 } } @Article{ ChoMeeWhi90, Author = { H.I. Choi and W.H. Meeks and B. White }, Title = { {A} rigidity theorem for property embedded minimal surfaces in {${\bf {R}}^3$} }, Journal = { J. Differential Geom. }, Volume = { 32 }, Pages = { 65-76 }, Year = { 1990 } } @Article{ ChoSch85, Author = { H.I. Choi and R. Schoen }, Title = { {T}he space of minimal embeddings of a surface into a three-dimensional manifold of positive {R}icci curvature }, Journal = { Invent.\ Math. }, Volume = { 81 }, Pages = { 387-394 }, Year = { 1985 } } @Misc{ ChoTre, Author = { H.I. Choi and A. Treibergs }, Title = { {M}ultiple harmonic diffeomorphisms from the complex plane to ideal polygons of the disk } } @Article{ ChoTre88, Author = { H.I. Choi and A. Treibergs }, Title = { {N}ew examples of harmonic diffeomorphisms of the hyperbolic plane into itself }, Journal = { Manuscripta Math. }, Volume = { 62 }, Pages = { 249-256 }, Year = { 1988 } } @Article{ ChoTre90, Author = { H.I. Choi and A. Treibergs }, Title = { {G}auss maps of spacelike constant mean curvature hypersurfaces of {M}inkowski space }, Journal = { J. Differential Geom. }, Volume = { 32 }, Pages = { 775-817 }, Year = { 1990 } } @Incollection{ ChoTre92, Author = { H.I. Choi and A. Treibergs }, Title = { {H}yperbolicity of constant mean curvature surfaces of {M}inkowski space }, Booktitle = { {P}roc.1st {P}acific {R}im {C}onf. {G}eom. {A}nal. }, Year = { 1992 } } @Incollection{ ChoTre93, Author = { H.I. Choi and A. Treibergs }, Title = { {C}onstructing harmonic maps into the hyperbolic space }, Booktitle = { {D}ifferential {G}eometry: partial differential equations on manifolds }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { American Math.\ Soc. }, Address = { Providence RI }, Volume = { 54:1 }, Pages = { 101-109 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ ChoWan83, Author = { H.I. Choi and A.N. Wang }, Title = { {A} first eigenvalue estimate for minimal hypersurfaces }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 559-562 }, Year = { 1983 } } @Article{ ChoKiKim94, Author = { S.M. Choi and U.H. Ki and H.J. Kim }, Title = { {C}omplete maximal space-like hypersurfaces in an anti-de-{S}itter space }, Journal = { Bull.\ Korean Math.\ Soc. }, Volume = { 31 }, Pages = { 85-92 }, Year = { 1994 } } @Article{ Cho86, Author = { Y. Choquet-Bruhat }, Title = { {A}pplications harmoniques hyperboliques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 303 }, Pages = { 109-113 }, Year = { 1986 } } @Article{ Cho87, Author = { Y. Choquet-Bruhat }, Title = { {G}lobal existence theorems for hyperbolic harmonic maps }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Phys.\ Th\'eor. }, Volume = { 46 }, Pages = { 97-111 }, Year = { 1987 } } @Article{ Cho88, Author = { Y. Choquet-Bruhat }, Title = { {G}lobal existence for nonlinear {$\sigma$}-models }, Journal = { Rend.\ Sem.\ Mat.\ Univ.\ Politec.\ Torino }, Pages = { 65-86 }, Year = { 1988 } } @Article{ ChoGil74, Author = { Y. Choquet-Bruhat and C. Gilain }, Title = { {D}iff\'eomorphismes harmoniques et unicit\'e }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 279 }, Pages = { 827-830 }, Year = { 1974 } } @Article{ ChoGu89, Author = { Y. Choquet-Bruhat and C.H. Gu }, Title = { {E}xistence globale d'applications harmoniques sur l'espace-temps de {M}inkowski {${M}_s$} }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 308 }, Pages = { 167-170 }, Year = { 1989 } } @Article{ ChoZhu95, Author = { K.S. Chou and X.F. Zhu }, Title = { {S}ome constancy results for nematic liquid crystals and harmonic maps }, Journal = { Analyse non-lin\'eaire }, Volume = { 12 }, Pages = { 99-115 }, Year = { 1995 } } @Misc{ ChoC, Author = { P. Chou{\'e} }, Title = { {A} regularity result for critical points of conformally invariant functionals } } @Article{ Cho91, Author = { B. Chow }, Title = { {T}he {R}icci-{H}amilton flow on the 2-sphere }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 325-334 }, Year = { 1991 } } @Article{ ChrTah, Author = { D. Christodoulou and A.S. Tahvildar }, Title = { {O}n the regularity of spherically symmetric wave-maps }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 46 }, Pages = { 1041-1091 } } @Article{ ChrTah93, Author = { D. Christodoulou and A.S. Tahvildar }, Title = { {O}n the asymptotic behaviour of spherically symmetric wave-maps }, Journal = { Duke Math.\ J. }, Volume = { 71 }, Pages = { 31-69 }, Year = { 1993 } } @Misc{ ChuKoh, Author = { I. Chung and S.E. Koh }, Title = { {A} note on the existence of harmonic and holomorphic maps } } @Article{ ChuKoh92, Author = { I. Chung and S.E. Koh }, Title = { {A} note on totally geodesic maps }, Journal = { Bull.\ Korean Math.\ Soc. }, Volume = { 29 }, Pages = { 233-236 }, Year = { 1992 } } @Book{ ChuNakSar77, Author = { L.O. Chung and M. Nakai and L. Sario and C. Wang }, Title = { {C}lassification theory of {R}iemannian manifolds }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 605 }, Series = { Lecture Notes in Math. }, Year = { 1977 } } @Article{ Cle86, Author = { C. Clement }, Title = { {S}tationary solutions in five-dimensional general relativity }, Journal = { Gen.\ Relativity Gravitation }, Volume = { 18 }, Pages = { 137-160 }, Year = { 1986 } } @Misc{ CohHarKin, Author = { R. Cohen and R. Hardt and D. Kinderlehrer and S.Y. Lin and M. Luskin }, Title = { {M}inimum energy configurations for liquid crystals: {C}omputational results } } @Article{ CoiLioMey93, Author = { R. Coifman and P.L. Lions and Y. Meyer and S. Semmer }, Title = { {C}ompensated compactness and {H}ardy spaces }, Journal = { J. Math.\ Pures Appl. }, Volume = { 72 }, Pages = { 247-286 }, Year = { 1993 } } @Article{ ColKen, Author = { A.G. Colares and K. Kenmotsu }, Title = { {I}sometric deformations of surfaces in {${\bf {R}}^3$} preserving the mean curvature function }, Journal = { Pacific J. Math. } } @Incollection{ ColJen91, Author = { B. Coleman and J.T. Jenkins }, Title = { {O}n a class of solutions in the theory of nematic phases }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 261-278 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Misc{ ConSan, Author = { S. Console and A. Sanini }, Title = { {G}auss maps generalized to normal and osculating spaces } } @Article{ ConCor65, Author = { C. Constantinescu and A. Cornea }, Title = { {C}ompactification of harmonic spaces }, Journal = { Nagoya Math.\ J. }, Volume = { 25 }, Pages = { 1-57 }, Year = { 1965 } } @Article{ Coq87, Author = { R. Coquereaux }, Title = { {C}omments about the geometry of nonlinear sigma models }, Journal = { Internat.\ J. Modern Phys.\ A }, Volume = { 2 }, Pages = { 1763-1772 }, Year = { 1987 } } @Article{ Cor56, Author = { H.O. Cordes }, Title = { \"{U}ber die eindeutige {B}estimmtheit der {L}\"osungen elliptischer {D}ifferentialgleichungen durch {A}nfangsvorgaben }, Journal = { Nachr.\ Akad.\ Wiss.\ G\"ottingen Math.-Phys.\ Kl.\ II }, Pages = { 239-258 }, Year = { 1956 } } @Article{ Cor88, Author = { K. Corlette }, Title = { {F}lat {${G}$}-bundles with canonical metrics }, Journal = { J. Differential Geom. }, Volume = { 28 }, Pages = { 361-382 }, Year = { 1988 } } @Article{ Cor91, Author = { K. Corlette }, Title = { {R}igid representations of {K}{\"a}hler fundamental groups }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 239-252 }, Year = { 1991 } } @Article{ Cor92, Author = { K. Corlette }, Title = { {A}rchimedean superrigidity and hyperbolic geometry }, Journal = { Ann.\ of Math. }, Volume = { 135 }, Pages = { 165-182 }, Year = { 1992 } } @Incollection{ Cor93, Author = { K. Corlette }, Title = { {N}onabelian {H}odge theory }, Booktitle = { {D}ifferential {G}eometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 54 part 2 }, Pages = { 125-144 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Incollection{ Cor95, Author = { K. Corlette }, Title = { {H}armonic maps, rigidity, and {H}odge theory }, Booktitle = { {P}roceedings of the {I}nternational {C}ongress of {M}athematicians }, Publisher = { Birkh\"auser Verlag }, Address = { Basel }, Pages = { 465-471 }, Year = { 1995 } } @Article{ CorZim94, Author = { K. Corlette and R.J. Zimmer }, Title = { {S}uperrigidity for cocycles and hyperbolic geometry }, Journal = { Internat.\ J. Math. }, Volume = { 5 }, Pages = { 273-290 }, Year = { 1994 } } @Misc{ Cor, Author = { J.-M. Coron }, Title = { {N}on unicit\'e des solutions faibles du probl\`eme de {C}auchy pour le flot des applications harmoniques } } @Incollection{ Cor86, Author = { J.-M. Coron }, Title = { {H}armonic maps from the disk into the euclidean {${N}$}-sphere }, Booktitle = { {N}onlinear functional analysis and its applications }, Editor = { F.E. Browder }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 45 }, Pages = { 301-304 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Unpublished{ Cor87, Author = { J.-M. Coron }, Title = { {O}n the singularities of harmonic maps from a domain in {${\bf {R}}^3$} into {${S}^2$} }, Note = { S\'em. 1986/87. Ecole Poly. Palaiseau }, Year = { 1987 } } @Article{ Cor90, Author = { J.-M. Coron }, Title = { {N}onuniqueness for the heat flow of harmonic maps }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 7 }, Pages = { 335-344 }, Year = { 1990 } } @Incollection{ Cor91A, Author = { J.-M. Coron }, Title = { {H}armonic maps with values into spheres }, Booktitle = { {P}roc. {I}.{C}.{M}. {K}yoto 1990, {I}{I} }, Publisher = { Springer }, Pages = { 1123-1135 }, Year = { 1991 } } @Article{ CorGhi89, Author = { J.-M. Coron and J.-M. Ghidaglia }, Title = { {E}xplosion en temps fini pour le flot des applications harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 308 }, Pages = { 339-344 }, Year = { 1989 } } @Article{ CorGul89, Author = { J.-M. Coron and R. Gulliver }, Title = { {M}inimizing {$p$}-harmonic maps into spheres }, Journal = { J. Reine Angew.\ Math. }, Volume = { 401 }, Pages = { 82-100 }, Year = { 1989 } } @Article{ CorHel89, Author = { J.-M. Coron and F. H{\'e}lein }, Title = { {H}armonic diffeomorphisms, minimizing harmonic maps and rotational symmetry }, Journal = { Compositio Math. }, Volume = { 69 }, Pages = { 175-228 }, Year = { 1989 } } @Article{ Cos84, Author = { C. Costa }, Title = { {E}xample of a complete minimal immersion in {${\bf {R}}^3$} of genus one and three embedded ends }, Journal = { Bull.\ Soc.\ Bras.\ Mat. }, Volume = { 15 }, Pages = { 47-54 }, Year = { 1984 } } @Article{ CosLia88, Author = { D. Costa and G. Liao }, Title = { {O}n removability of a singular submanifold for weakly harmonic maps }, Journal = { J. Fac.\ Sci.\ Univ.\ Tokyo Sect.\ IA Math. }, Volume = { 35 }, Pages = { 321-344 }, Year = { 1988 } } @Misc{ CouGla, Author = { P. Coulton and J.F. Glazebrook }, Title = { {S}ubmanifolds of the {C}ayley projective plane with bounded second fundamental form } } @Article{ Cou40, Author = { R. Courant }, Title = { {T}he existence of minimal surfaces of given topological type }, Journal = { Acta Math. }, Volume = { 72 }, Pages = { 51-98 }, Year = { 1940 } } @Article{ Cou41, Author = { R. Courant }, Title = { {C}ritical points and unstable minimal surfaces }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 27 }, Pages = { 51-57 }, Year = { 1941 } } @Book{ Cou50, Author = { R. Courant }, Title = { {D}irichlet's principle, conformal mappings and minimal surfaces }, Publisher = { Interscience }, Volume = { III }, Series = { Pure Appl.\ Math. }, Year = { 1950 } } @Article{ CraSau86, Author = { M. Crampin and D.J. Saunders }, Title = { {T}he sine-{G}ordon equation, {T}chebychev nets, and harmonic maps }, Journal = { Rep.\ Math.\ Phys. }, Volume = { 23 }, Pages = { 327-340 }, Year = { 1986 } } @Article{ Cra93, Author = { T.A. Crawford }, Title = { {F}ull holomorphic maps from the {R}iemann sphere to complex projective space }, Journal = { J. Differential Geom. }, Volume = { 38 }, Pages = { 161-190 }, Year = { 1993 } } @Unpublished{ Cra95, Author = { T.A. Crawford }, Title = { {T}he space of harmonic maps from the {$2$}-sphere to the complex projective space }, Note = { McGill preprint }, Year = { 1995 } } @Article{ Cro87, Author = { C. Croke }, Title = { {L}ower bounds on the energy of maps }, Journal = { Duke Math.\ J. }, Volume = { 55 }, Pages = { 901-908 }, Year = { 1987 } } @Article{ CroFat90, Author = { C. Croke and A. Fathi }, Title = { {A}n inequality between energy and intersection }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 22 }, Pages = { 489-494 }, Year = { 1990 } } @Article{ CsiFitOks, Author = { L. Csink and P.J. Fitzsimmons and B. {\O}ksendal }, Title = { {A} stochastic interpretation of harmonic morphisms }, Journal = { Math.\ Ann. } } @Article{ CsiOks83, Author = { L. Csink and B. {\O}ksendal }, Title = { {S}tochastic harmonic morphisms : {F}unctions mapping the paths of one diffusion into the paths of another }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 33 }, Pages = { 219-240 }, Year = { 1983 } } @Incollection{ CsiOks88, Author = { L. Csink and B. {\O}ksendal }, Title = { {H}armonic morphisms and ray processes }, Booktitle = { {P}otential theory ({P}rague) }, Publisher = { Plenum }, Address = { New York, London }, Pages = { 71-74 }, Year = { 1988 } } @Article{ Cuk, Author = { F. Cukierman }, Title = { {R}igidity of isotropic immersions }, Journal = { Math.\ Z. } } @Article{ DAmTot, Author = { G. D'Ambra and G. Toth }, Title = { {O}n infinitesimal and local rigidity of harmonic maps between spheres defined by spherical harmonics }, Journal = { Ann.\ di Mat. } } @Article{ DAmTot84, Author = { G. D'Ambra and G. Toth }, Title = { {E}xtrinsic rigidity for equivariant harmonic maps into spheres }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 6 }, Pages = { 249-255 }, Year = { 1984 } } @Article{ DAmTot84A, Author = { G. D'Ambra and G. Toth }, Title = { {P}arameter space for harmonic maps of constant energy density into spheres }, Journal = { Geom.\ Dedicata }, Volume = { 4 }, Pages = { 61-67 }, Year = { 1984 } } @Unpublished{ DaiShoUra94, Author = { Y.J. Dai and M. Shoji and H. Urakawa }, Title = { {H}armonic maps into {L}ie groups }, Note = { Preprint }, Year = { 1994 } } @Article{ DajGro85, Author = { M. Dajczer and D. Gromoll }, Title = { {R}eal {K}\"ahler manifolds and uniqueness of the {G}auss map }, Journal = { J. Differential Geom. }, Volume = { 22 }, Pages = { 13-28 }, Year = { 1985 } } @Article{ DajRod86, Author = { M. Dajczer and L. Rodriguez }, Title = { {R}igidity of real {K}aehler submanifolds }, Journal = { Duke Math.\ J. }, Volume = { 53 }, Pages = { 211-220 }, Year = { 1986 } } @Article{ DajRod94, Author = { M. Dajczer and L. Rodriguez }, Title = { {O}n isometric immersions into complex space forms }, Journal = { Math.\ Ann. }, Volume = { 299 }, Pages = { 223-230 }, Year = { 1994 } } @Article{ DajTho87, Author = { M. Dajczer and G. Thorbergsson }, Title = { {H}olomorphicity of minimal submanifolds in complex space forms }, Journal = { Math.\ Ann. }, Volume = { 227 }, Pages = { 353-360 }, Year = { 1987 } } @Article{ DamRic92, Author = { E. Damek and F. Ricci }, Title = { {A} class of nonsymmetric harmonic {R}iemannian spaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 27 }, Pages = { 139-142 }, Year = { 1992 } } @Article{ Dao77, Author = { Dao~Chong~Thi }, Title = { {M}inimal real currents on compact {R}iemannian manifolds }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 41:4 }, Year = { 1977 } } @Article{ Dao80, Author = { Dao~Chong~Thi }, Title = { {M}ultivarifolds and the classical multidimensional {P}lateau problem }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 44 }, Pages = { 1031-1065 }, Year = { 1980 } } @Article{ Dao85, Author = { Dao~Chong~Thi }, Title = { {G}lobally minimal currents and surfaces in {R}iemannian manifolds }, Journal = { Acta Math.\ Vietnam }, Volume = { 10 }, Pages = { 296-333 }, Year = { 1985 } } @Incollection{ Dao85A, Author = { Dao~Chong~Thi }, Title = { {M}ultidimensional parametrized variational problems on {R}iemannian manifolds }, Booktitle = { {A}pplications of topology in modern anlaysis }, Publisher = { Gos.\ Univ.\ Voronezh. }, Pages = { 63-86, 176 }, Note = { (Russsian) }, Series = { Novoe Global Anal. }, Year = { 1985 } } @Incollection{ Dao86, Author = { Dao~Chong~Thi }, Title = { {M}ultidimensional parametrized variational problems on {R}iemannian manifolds }, Booktitle = { {G}lobal {A}nalysis - {S}tudies and {A}pplications {I}{I} }, Editor = { Y.G. Borisovich and Y.E. Gliklikh }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1214 }, Series = { Lecture Notes in Math. }, Year = { 1986 } } @Article{ Dao91, Author = { Dao~Chong~Thi }, Title = { {L}agangian gauges and globally minimal {L}agrangian submanifolds in {H}ermitian manifolds }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 24 }, Pages = { 44-48 }, Year = { 1991 } } @Incollection{ DaoFom84, Author = { Dao~Chong~Thi and A.T. Fomenko }, Title = { {T}opology of absolute minima of functionals of volume type and the {D}irichlet functional }, Booktitle = { {C}urrent problems in real and complex analysis }, Publisher = { Acad.\ Nauk.\ Ukrain SSR }, Address = { Kiev }, Volume = { 150 }, Pages = { 40-64 }, Year = { 1984 } } @Book{ DaoFom91, Author = { Dao~Chong~Thi and A.T. Fomenko }, Title = { {M}inimal surfaces, stratified multivarifolds and the {P}lateau problem }, Publisher = { American Math.\ Soc. }, Address = { Providence RI }, Volume = { 84 }, Series = { Transl.\ Math.\ Monographs }, Year = { 1991 } } @Incollection{ Dar82, Author = { R.W.R. Darling }, Title = { {M}artingales in manifolds -- {D}efinition, {E}xamples and behaviour under maps }, Booktitle = { {S}\'eminaire de {P}robabilit\'es {X}{V}{I} 1980/91 {S}uppl\'ement: {G}\'eom\'etrie diff\'erentielle stochastique }, Editor = { J. Az{\'e}ma and M. Yor }, Publisher = { Springer }, Address = { Berlin }, Volume = { 921 }, Pages = { 217-236 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Incollection{ DavGraska94, Author = { J. Davidov and G. Grantcharov and O. Mu{\v s}karov }, Title = { {A}lmost complex structures on twistor spaces }, Booktitle = { {A}lmost complex structures }, Editor = { S. Dimiev and K. Sekigawa }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 113-149 }, Year = { 1994 } } @Article{ DavSer93, Author = { J. Davidov and A.G. Sergeev }, Title = { {T}wistor spaces and harmonic maps }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 48:3 }, Pages = { 3-96 }, Year = { 1993 } } @Article{ Davska88, Author = { J. Davidov and O. Mu{\v s}karov }, Title = { {T}he existence of holomorphic functions on twistor spaces }, Journal = { Bull.\ Soc.\ Math.\ Belg.\ S\'er.\ B }, Volume = { 40 }, Pages = { 131-151 }, Year = { 1988 } } @Article{ Davska90, Author = { J. Davidov and O. Mu{\v s}karov }, Title = { {T}wistor spaces with {H}ermitian {R}icci tensor }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 109 }, Pages = { 1115-1120 }, Year = { 1990 } } @Article{ Davska91, Author = { J. Davidov and O. Mu{\v s}karov }, Title = { {O}n the {R}iemannian curvature of a twistor space }, Journal = { Acta Math.\ Hungar. }, Volume = { 58 }, Pages = { 319-322 }, Year = { 1991 } } @Article{ Davska94, Author = { J. Davidov and O. Mu{\v s}karov }, Title = { {O}n the {R}iemannian curvature of a twistor space ({C}orrection) }, Journal = { Acta Math.\ Hungar. }, Volume = { 65 }, Pages = { 421-422 }, Year = { 1994 } } @Article{ Dav42, Author = { N. Davids }, Title = { {M}inimal surfaces spanning closed manifolds and having prescribed topological position }, Journal = { Amer.\ J. Math. }, Volume = { 64 }, Pages = { 348-362 }, Year = { 1942 } } @Article{ daS87, Author = { A.M. da~Silveira }, Title = { {S}tability of complete noncompact surfaces with constant mean curvature }, Journal = { Math.\ Ann. }, Volume = { 277 }, Pages = { 629-638 }, Year = { 1987 } } @Article{ Del41, Author = { C. Delaunay }, Title = { {S}ur la surface de r\'evolution dont la courbure moyenne est constante (avec une note de {S}turm) }, Journal = { J. Math.\ Pures Appl. }, Volume = { 6 }, Pages = { 309-320 }, Year = { 1841 } } @Article{ Dem90, Author = { F. Demengel }, Title = { {U}ne caract{\'e}risation des applications de {${W}^{1,p}({B}^{N},{S}^1)$} qui peuvent \^etre approch{\'e}es par des fonctions r{\'e}guli{\`e}res }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 310 }, Pages = { 553-557 }, Year = { 1990 } } @Article{ DemHad90, Author = { F. Demengel and R. Hadiji }, Title = { {R}elaxed energies for functionals on {${W}^{1,1}({B}^2,{S}^1)$} }, Journal = { J. Nonlin.\ Anal. }, Volume = { 19 }, Pages = { 625-641 }, Year = { 1990 } } @Article{ DerEriKar86, Author = { T. Derali and A. Eriz and A. Karasu }, Title = { {H}armonic maps and magnetostatic axially symmetric solution of the {K}aluza--{K}lein theory }, Journal = { Nuovo Cimento B }, Volume = { 93 }, Pages = { 102-112 }, Year = { 1986 } } @Article{ DeTKaz81, Author = { D. DeTurck and J.L. Kazdan }, Title = { {S}ome regularity theorems in {R}iemannian geometry }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 14 }, Pages = { 249-260 }, Year = { 1981 } } @Article{ DeTZil92, Author = { D. DeTurck and W. Ziller }, Title = { {M}inimal isometric immersions of spherical space forms in spheres }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 67 }, Pages = { 428-458 }, Year = { 1992 } } @Incollection{ DeTZil93, Author = { D. DeTurck and W. Ziller }, Title = { {S}pherical minimal immersions of spherical space forms }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 111-120 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ deA83, Author = { S.C. de~Almeida }, Title = { {M}inimal hypersurfaces of {${S}^4$} with non-zero {G}auss--{K}ronecker curvature }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 14 }, Pages = { 137-146 }, Year = { 1983 } } @Article{ deAIzqZak92, Author = { J.A. de~Azc{\'a}rraga and J.M. Izquierdo and W.J. Zakrzewski }, Title = { {M}odels with {H}opf term }, Journal = { J. Math.\ Phys. }, Volume = { 33 }, Pages = { 1272-1280 }, Year = { 1992 } } @Article{ deAIzqZak92A, Author = { J.A. de~Azc{\'a}rraga and J.M. Izquierdo and W.J. Zakrzewski }, Title = { {A} supergroup based supersigma model }, Journal = { J. Math.\ Phys. }, Volume = { 33 }, Pages = { 2357-2364 }, Year = { 1992 } } @Article{ deB82, Author = { P. de~Bartolomeis }, Title = { {S}ur l'analyticit{\'e} complexe de certaines applications harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 284 }, Pages = { 525-527 }, Year = { 1982 } } @Incollection{ deB83, Author = { P. de~Bartolomeis }, Title = { {S}ur l'analyticit\'e complexe de certaines applications harmoniques ({I}{I}) }, Booktitle = { {S}\'eminaire d'{A}nalyse {P}. {L}elong--{P}. {D}olbeault--{H}. {S}koda. {A}nn\'ees 1981/1983 }, Editor = { P. Lelong and P. Dolbeault and H. Skoda }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1028 }, Pages = { 27-40 }, Series = { Lecture Notes in Math. }, Year = { 1983 } } @Incollection{ deB91, Author = { P. de~Bartolomeis }, Title = { {S}ome new global results in twistor geometry }, Booktitle = { {G}eometry and complex variables }, Publisher = { Dekker }, Volume = { 132 }, Pages = { 155-163 }, Series = { Lecture Notes in Pure and Appl.\ Math. }, Year = { 1991 } } @Incollection{ deB93, Author = { P. de~Bartolomeis }, Title = { {T}wistor constructions for vector bundles }, Booktitle = { {C}omplex analysis and geometry }, Publisher = { Plenum }, Address = { New York }, Pages = { 103-114 }, Series = { Univ.\ Ser.\ Math. }, Year = { 1993 } } @Incollection{ deBBur86, Author = { P. de~Bartolomeis and D. Burns }, Title = { {S}table harmonic maps with values in {${P}^m{C}$} }, Booktitle = { {M}iniconference on operator theory and {P}{D}{E}'s ({N}orth {R}yde 1985) }, Volume = { 14 }, Pages = { 111-116 }, Series = { Proc.\ Cent.\ Math.\ Austral.\ Nat.\ Univ. }, Year = { 1986 } } @Article{ deBBur88, Author = { P. de~Bartolomeis and D. Burns }, Title = { {A}pplications harmoniques stables dans {${\bf {P}}^n$} }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 22 }, Pages = { 159-177 }, Year = { 1988 } } @Article{ deBBur88A, Author = { P. de~Bartolomeis and D. Burns }, Title = { {S}tability of vector bundles and extremal metrics }, Journal = { Invent.\ Math. }, Volume = { 92 }, Pages = { 403-477 }, Year = { 1988 } } @Incollection{ deBBur88B, Author = { P. de~Bartolomeis and D. Burns }, Title = { {S}table harmonic maps to {${\bf {P}}^n$} }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Year = { 1988 } } @Article{ deBBurBur89, Author = { P. de~Bartolomeis and D. Burns and F.E. Burstall and J. Rawnsley }, Title = { {S}tability of harmonic maps of {K}\"ahler manifolds }, Journal = { J. Differential Geom. }, Volume = { 30 }, Pages = { 579-594 }, Year = { 1989 } } @Article{ deBDer88, Author = { P. de~Bartolomeis and M. Derridj }, Title = { {P}ositive vector bundles and harmonic maps }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 150 }, Pages = { 21-37 }, Year = { 1988 } } @Article{ deBMigNan88, Author = { P. de~Bartolomeis and L. Migliorini and A. Nannicini }, Title = { {E}spaces de twisteurs k{\"a}hl{\'e}riens }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 307 }, Pages = { 259-261 }, Year = { 1988 } } @Article{ DeG73, Author = { E. De~Giorgi }, Title = { {P}roblemi di superfici minime con ostacoli: forma non cartesiana }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 8 }, Pages = { 80-88 }, Year = { 1973 } } @Article{ deO86, Author = { M.E.G.G. de~Oliveira }, Title = { {S}ome new examples of nonorientable minimal surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 98 }, Pages = { 629-636 }, Year = { 1986 } } @Article{ DeOEli86, Author = { M. De~Oliveira and G.G. Elisa }, Title = { {S}ome new examples of nonorientable minimal surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 98 }, Pages = { 629-636 }, Year = { 1986 } } @Article{ Dia82, Author = { C.C. Dias }, Title = { {I}sometric immersions with slow growth of curvature }, Journal = { An.\ Acad.\ Brasil.\ Ci\^enc. }, Volume = { 54 }, Pages = { 293-295 }, Year = { 1982 } } @Article{ DieOhs85, Author = { K. Diederich and T. Ohsawa }, Title = { {H}armonic mappings and disc bundles over compact {K}\"ahler manifolds }, Journal = { Publ.\ Res.\ Inst.\ Math.\ Sci. }, Volume = { 21 }, Pages = { 819-833 }, Year = { 1985 } } @Misc{ Die, Author = { U. Dierkes }, Title = { {A} geometric maximum principle for surfaces of prescribed mean curvature in {R}iemannian manifolds } } @Misc{ DieA, Author = { U. Dierkes }, Title = { {M}aximum principles and nonexistence results for minimal submanifolds } } @Article{ Die93, Author = { U. Dierkes }, Title = { {A} {B}ernstein result for energy minimizing hypersurfaces }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 37-54 }, Year = { 1993 } } @Book{ DieHilKus92, Author = { U. Dierkes and S. Hildebrandt and A. K{\"u}ster and O. Wohlrab }, Title = { {M}inimal surfaces. {I} }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 295 }, Series = { Grundlehren Math.\ Wiss. }, Year = { 1992 } } @Book{ DieHilKus92A, Author = { U. Dierkes and S. Hildebrandt and A. K{\"u}ster and O. Wohlrab }, Title = { {M}inimal surfaces. {I}{I} }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 296 }, Series = { Grundlehren Math.\ Wiss. }, Year = { 1992 } } @Article{ DieHilLew87, Author = { U. Dierkes and S. Hildebrandt and H. Lewy }, Title = { {O}n the analyticity of minimal surfaces at movable boundaries of prescribed length }, Journal = { J. Reine Angew.\ Math. }, Volume = { 379 }, Pages = { 100-114 }, Year = { 1987 } } @Article{ Dil87, Author = { F. Dillen }, Title = { {M}inimal immersions of surfaces into spheres }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 49 }, Pages = { 94-96 }, Year = { 1987 } } @Article{ Dim92, Author = { I. Dimitric }, Title = { {S}ubmanifolds of {${E}^m$} with harmonic mean curvature vector }, Journal = { Bull.\ Inst.\ Math.\ Acad.\ Sinica }, Volume = { 20 }, Pages = { 53-65 }, Year = { 1992 } } @Incollection{ Din80, Author = { A.M. Din }, Title = { {C}lassical solutions of nonlinear {$\sigma$}-models and their quantum fluctuations }, Booktitle = { {G}roup theoretical methods in physics }, Publisher = { Springer }, Address = { Berlin }, Volume = { 135 }, Pages = { 283-294 }, Series = { Lecture Notes in Phys. }, Year = { 1980 } } @Incollection{ Din80A, Author = { A.M. Din }, Title = { {N}on-linear techniques in two-dimensional {G}rassmannian sigma models }, Booktitle = { {G}roup theoretical methods in physics }, Publisher = { Springer }, Address = { Berlin }, Volume = { 135 }, Series = { Lecture Notes in Phys. }, Year = { 1980 } } @Article{ DinHorZak84, Author = { A.M. Din and Z. Horvath and W.J. Zakrzewski }, Title = { {T}he {R}iemann--{H}ilbert {P}roblem and finite action {${\bf {C}}{P}^{n-1}$} model solutions }, Journal = { Nuclear Phys.\ B }, Volume = { 233 }, Pages = { 269-288 }, Year = { 1984 } } @Misc{ DinZak, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {F}ermion solutions in the supersymmetric {${\bf {C}}{P}^{n-1}$} model } } @Misc{ DinZakA, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {Q}uantum fluctuations around a non-instanton solution } } @Unpublished{ DinZak79, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {E}mbeddings of classical solutions of {${O}(2p+1)$} non-linear {$\sigma$}-models in {${\bf {C}}{P}^{n-1}$} models }, Note = { CERN preprint }, Year = { 1979 } } @Unpublished{ DinZak79A, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {S}tability properties of classical solutions to non-linear {$\sigma$}-models }, Note = { CERN preprint }, Year = { 1979 } } @Article{ DinZak80, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {G}eneral classical solutions in the {${\bf {C}}{P}^{n-1}$} model }, Journal = { Nuclear Phys.\ B }, Volume = { 174 }, Pages = { 397-406 }, Year = { 1980 } } @Article{ DinZak80A, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {P}roperties of the general classical {${\bf {C}}{P}^{n-1}$} model }, Journal = { Phys.\ Lett. }, Volume = { 95 }, Pages = { 419-422 }, Year = { 1980 } } @Article{ DinZak81, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {C}lassical solutions in {G}rassmannian {$\sigma$}-models }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 5 }, Pages = { 553-561 }, Year = { 1981 } } @Article{ DinZak83, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {S}ome properties of classical solutions in grassmannian sigma models }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 7 }, Pages = { 505-??? }, Year = { 1983 } } @Article{ DinZak84, Author = { A.M. Din and W.J. Zakrzewski }, Title = { {F}urther properties of classical solutions in {G}rassmannian {$\sigma$}-models }, Journal = { Nuclear Phys.\ B }, Volume = { 237 }, Pages = { 461-476 }, Year = { 1984 } } @Incollection{ Din93, Author = { Q. Ding }, Title = { {T}he {D}irichlet problem at infinity for manifolds of nonpositive curvature }, Booktitle = { {D}ifferential {G}eometry ({S}hanghai, 1991) }, Publisher = { World Sci.\ Publishing }, Address = { River Edge, NJ }, Pages = { 49-58 }, Year = { 1993 } } @Article{ Din96, Author = { Q. Ding }, Title = { {T}he {C}auchy problem for harmonic maps from two-dimensional curved {L}orentzian manifolds }, Journal = { Chinese J. Contemp.\ Math. }, Volume = { 17 }, Pages = { 59--66 }, Year = { 1996 } } @Article{ Din96A, Author = { Q. Ding }, Title = { {T}he {C}auchy problem for harmonic maps on two-dimensional curved {L}orentzian manifolds }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 17 }, Pages = { 73-78 }, Note = { (Chinese, Chinese summary) }, Year = { 1996 } } @Article{ DinWan96, Author = { Q. Ding and J. Wang }, Title = { {A} remark on harmonic maps between pseudo-{R}iemannian spheres }, Journal = { Northeast.\ Math.\ J. }, Volume = { 12 }, Pages = { 217--221 }, Year = { 1996 } } @Misc{ Din, Author = { W.Y. Ding }, Title = { {O}n the heat flow method for harmonic maps } } @Article{ Din86, Author = { W.Y. Ding }, Title = { {L}usternik--{S}chnirelmann theory for harmonic maps }, Journal = { Acta Math.\ Sinica }, Volume = { 2 }, Pages = { 105-122 }, Year = { 1986 } } @Article{ Din88, Author = { W.Y. Ding }, Title = { {S}ymmetric harmonic maps between spheres }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 118 }, Pages = { 641-649 }, Year = { 1988 } } @Article{ Din90, Author = { W.Y. Ding }, Title = { {B}low-up of solutions of heat flows for harmonic maps }, Journal = { Chinese Adv.\ in Math. }, Volume = { 19 }, Pages = { 80-92 }, Year = { 1990 } } @Incollection{ Din92, Author = { W.Y. Ding }, Title = { {S}ome recent results on the heat flow of harmonic maps }, Booktitle = { {N}onlinear analysis and microlocal analysis }, Editor = { K.C. Chang et al }, Publisher = { World Sci.\ Publ. }, Address = { Singapore }, Pages = { 44-56 }, Year = { 1992 } } @Article{ Din94, Author = { W.Y. Ding }, Title = { {H}armonic {H}opf constructions between spheres }, Journal = { Internat.\ J. Math. }, Volume = { 5 }, Pages = { 849-860 }, Year = { 1994 } } @Article{ Din94A, Author = { W.Y. Ding }, Title = { {L}ocally minimizing harmonic maps from noncompact manifolds }, Journal = { Manuscripta Math. }, Volume = { 85 }, Pages = { 283-297 }, Year = { 1994 } } @Misc{ DinLi, Author = { W.Y. Ding and Jiayu Li }, Title = { {A} new proof of {H}amilton's theorem on harmonic maps from manifolds with boundary } } @Article{ DinLin92, Author = { W.Y. Ding and F.H. Lin }, Title = { {A} generalization of {E}ells--{S}ampson's theorem }, Journal = { J. Partial Differential Equations }, Volume = { 5 }, Pages = { 13-22 }, Year = { 1992 } } @Article{ DinTia95, Author = { W.Y. Ding and G. Tian }, Title = { {E}nergy identity for a class of approximate harmonic maps from surfaces }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 3 }, Pages = { 543-554 }, Year = { 1995 } } @Incollection{ DinWan93, Author = { W.Y. Ding and G.F. Wang }, Title = { {N}onexistence of smooth axially symmetric harmonic maps from {${B}^3$} into {${S}^2$} }, Booktitle = { {N}onlinear partial differential equations }, Editor = { G. Dong and F.H. Lin }, Publisher = { Intern.\ Academic Publ. }, Pages = { 38-45 }, Year = { 1993 } } @Article{ DinWan91, Author = { W.Y. Ding and Y.D. Wang }, Title = { {H}armonic maps of complete noncompact {R}iemannian manifolds }, Journal = { Internat.\ J. Math. }, Volume = { 2 }, Pages = { 617-633 }, Year = { 1991 } } @Article{ DodVanVaz87, Author = { C.T.J. Dodson and L. Vanhecke and M.E. Vazquez-Abal }, Title = { {H}armonic geodesic symmetries }, Journal = { C. R. Math.\ Rep.\ Acad.\ Sci.\ Canada }, Volume = { 9 }, Pages = { 231-235 }, Year = { 1987 } } @Article{ DodVaz, Author = { C.T.J. Dodson and M.E. Vazquez-Abal }, Title = { {I}nduced harmonic mappings of tangent bundles and frame bundles }, Journal = { Mat.\ Zametki }, Volume = { 3 }, Pages = { 27-37 }, Note = { (Russian) } } @Misc{ DodVazA, Author = { C.T.J. Dodson and M.E. Vazquez-Abal }, Title = { {O}n bundle projection and prolongation of harmonicity } } @Article{ DodVaz90, Author = { C.T.J. Dodson and M.E. Vazquez-Abal }, Title = { {H}armonic fibrations of the tangent bundle of order two }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 4 }, Pages = { 943-952 }, Year = { 1990 } } @Unpublished{ Dol95, Author = { A. Doliwa }, Title = { {H}olomorphic curves and {T}oda systems }, Note = { Warsaw preprint }, Year = { 1995 } } @Unpublished{ DolSym92, Author = { A. Doliwa and A. Sym }, Title = { {M}inimal surfaces in {${S}^{2m}$} and {T}oda systems }, Note = { Warsaw preprint }, Year = { 1992 } } @Article{ DolSym94, Author = { A. Doliwa and A. Sym }, Title = { {N}on-linear {$\sigma$}-models on spheres and {T}oda systems }, Journal = { Phys.\ Lett.\ A }, Volume = { 185 }, Pages = { 453-460 }, Year = { 1994 } } @Article{ Dom62, Author = { P. Dombrowski }, Title = { {O}n the geometry of the tangent bundle }, Journal = { J. Reine Angew.\ Math. }, Volume = { 210 }, Pages = { 73-88 }, Year = { 1962 } } @Incollection{ Don84, Author = { S.K. Donaldson }, Title = { {G}auge theory and topology }, Booktitle = { {P}roc. {I}ntern. {C}ong. {M}ath. {W}arsaw 1983 }, Publisher = { PWN }, Address = { Warsaw }, Pages = { 641-645 }, Year = { 1984 } } @Article{ Don84A, Author = { S.K. Donaldson }, Title = { {I}nstantons and geometric invariant theory }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 93 }, Pages = { 453-460 }, Year = { 1984 } } @Incollection{ Don84B, Author = { S.K. Donaldson }, Title = { {T}he {Y}ang--{M}ills equations on euclidean space }, Booktitle = { {P}rospects in {M}ath. {O}berwolfach {A}nniv. }, Publisher = { Birkh\"auser }, Pages = { 93-109 }, Year = { 1984 } } @Article{ Don87, Author = { S.K. Donaldson }, Title = { {T}wisted harmonic maps and the self-duality equations }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 55 }, Pages = { 127-131 }, Year = { 1987 } } @Article{ Don92, Author = { S.K. Donaldson }, Title = { {B}oundary value problems for {Y}ang-{M}ills fields }, Journal = { J. Geom.\ Phys. }, Volume = { 8 }, Pages = { 89-122 }, Year = { 1992 } } @Misc{ Don, Author = { Y.X. Dong }, Title = { {T}he {G}auss map of submanifolds in {${C}{P}^n$} } } @Unpublished{ DonA, Author = { Y.X. Dong }, Title = { {H}armonic maps and morphisms from spheres and deformed spheres }, Note = { Preprint } } @Unpublished{ DonB, Author = { Y.X. Dong }, Title = { {H}armonic maps between spheres and ellipsoids via {H}opf constructions }, Note = { to appear } } @Article{ Don92A, Author = { Y.X. Dong }, Title = { {O}n the isotropy of harmonic maps from surfaces to complex projective spaces }, Journal = { Internat.\ J. Math. }, Volume = { 3 }, Pages = { 165-177 }, Year = { 1992 } } @Article{ Don97, Author = { Y.X. Dong }, Title = { {B}erstein theorem for harmonic morphisms from {$({N}+1)$}-sphere to {${N}$}-manifold }, Journal = { Chinese Sci.\ Bull. }, Volume = { 42 }, Pages = { 11-14 }, Year = { 1997 } } @Misc{ DonShe, Author = { Y.X. Dong and Y.B. Shen }, Title = { {O}n factorization theorems of harmonic maps into {${U}({N})$} and minimal uniton numbers } } @Misc{ DonSheA, Author = { Y.X. Dong and Y.B. Shen }, Title = { {O}n twistor {G}auss maps of surfaces in {$4$}-spheres } } @Unpublished{ DonSheB, Author = { Y.X. Dong and Y.B. Shen }, Title = { {P}luriharmonic maps from compact {K}aehler manifolds with positive first {C}hern class into quaternionic projective spaces }, Note = { preprint } } @Article{ DonShe96, Author = { Y.X. Dong and Y.B. Shen }, Title = { {F}actorization and uniton numbers for harmonic maps into the unitary group {${U}({N})$} }, Journal = { Sci.\ China Ser.\ A }, Volume = { 39 }, Pages = { 589--597 }, Year = { 1996 } } @Article{ Don77, Author = { H. Donnelly }, Title = { {S}pectral invariants of the second variation operator }, Journal = { Illinois J. Math. }, Volume = { 21 }, Pages = { 185-189 }, Year = { 1977 } } @Article{ Don86, Author = { H. Donnelly }, Title = { {B}ounded harmonic functions and positive {R}icci curvature }, Journal = { Math.\ Z. }, Volume = { 191 }, Pages = { 559-565 }, Year = { 1986 } } @Article{ Don94, Author = { H. Donnelly }, Title = { {D}irichlet problem at infinity for harmonic maps - rank one symmetric spaces }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 344 }, Pages = { 713-736 }, Year = { 1994 } } @Article{ DonGigVan90, Author = { S. Donnini and G. Gigante and L. Vanhecke }, Title = { {H}armonic reflections with respect to submanifolds }, Journal = { Illinois J. Math. }, Volume = { 34 }, Pages = { 78-86 }, Year = { 1990 } } @Misc{ Dor, Author = { J. Dorfmeister }, Title = { {W}eighted {$l_1$}-{G}rassmannians and {B}anach manifolds of solutions of the {${K}{P}$}-equation and the {${K}d{V}$}-equation } } @Unpublished{ DorHaa94, Author = { J. Dorfmeister and G. Haak }, Title = { {M}eromorphic potentials and smooth {C}{M}{C} surfaces }, Note = { Kansas preprint }, Year = { 1994 } } @Unpublished{ DorHaa96, Author = { J. Dorfmeister and G. Haak }, Title = { {O}n constant mean curvature surfaces with periodic metric }, Note = { Preprint }, Year = { 1996 } } @Unpublished{ DorHaa96A, Author = { J. Dorfmeister and G. Haak }, Title = { {O}n symmetries of constant mean curvature surfaces }, Note = { Preprint }, Year = { 1996 } } @Article{ DorMcIPed97, Author = { J. Dorfmeister and I. McIntosh and F. Pedit and H. Wu }, Title = { {O}n the meromorphic potential for a harmonic surface in a {$k$}-symmetric space }, Journal = { Manuscripta Math. }, Volume = { 92 }, Pages = { 143--152 }, Year = { 1997 } } @Misc{ DorNeh, Author = { J. Dorfmeister and E. Neher }, Title = { {I}soparametric hypersurfaces, case {$g=6$}, {$m=1$} } } @Unpublished{ DorPedWu93, Author = { J. Dorfmeister and F. Pedit and H. Wu }, Title = { {W}eierstrass type representation of harmonic maps into symmetric spaces }, Note = { Preprint }, Year = { 1993 } } @Article{ DorWu93, Author = { J. Dorfmeister and H. Wu }, Title = { {C}onstant mean curvature surfaces and loop groups }, Journal = { J. Reine Angew.\ Math. }, Volume = { 440 }, Pages = { 43-76 }, Year = { 1993 } } @Unpublished{ Dor86, Author = { C.M. Doria }, Title = { {E}xistence of harmonic-conformal representatives for some classes of maps from compact planar domains with free boundary }, Note = { Preprint, Univ. of Warwick }, Year = { 1986 } } @Unpublished{ Dor88, Author = { C.M. Doria }, Title = { {O}n existence of minimal surfaces with free boundary }, Note = { Thesis, Univ. of Warwick }, Year = { 1988 } } @Article{ Dou31, Author = { J. Douglas }, Title = { {S}olution to the problem of {P}lateau }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 33 }, Pages = { 263-321 }, Year = { 1931 } } @Article{ Dou32, Author = { J. Douglas }, Title = { {O}ne sided minimal surfaces with a given boundary }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 34 }, Pages = { 731-756 }, Year = { 1932 } } @Article{ Dou33, Author = { J. Douglas }, Title = { {T}he problem of {P}lateau }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Year = { 1933 } } @Article{ Dou36, Author = { J. Douglas }, Title = { {S}ome new results in the problem of {P}lateau }, Journal = { J. Math.\ Phys. }, Volume = { 15 }, Pages = { 55-64 }, Year = { 1936 } } @Article{ Dou39, Author = { J. Douglas }, Title = { {M}inimal surfaces of higher topological structure }, Journal = { Ann.\ of Math. }, Volume = { 40 }, Pages = { 205-298 }, Year = { 1939 } } @Incollection{ doC80, Author = { M. do~Carmo }, Title = { {M}inimal surfaces: stability and finiteness }, Booktitle = { {P}roc. {I}nternat. {C}ongress {M}ath. {H}elsinki 1978 }, Editor = { O. Lehto }, Publisher = { I.C.M., Helsinki }, Address = { Helsinki }, Pages = { 401-405 }, Year = { 1980 } } @Incollection{ doC78, Author = { M.P. do~Carmo }, Title = { {H}armonic mappings }, Booktitle = { {P}roc. 10th {B}razilian {M}ath. {C}olloq., {I} }, Pages = { 77-99 }, Year = { 1978 } } @Incollection{ doC81, Author = { M.P. do~Carmo }, Title = { {S}tability of minimal submanifolds }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Editor = { D. Ferus and W. K{\"u}hnel and U. Simon and B. Wegner }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 838 }, Pages = { 129-139 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Incollection{ doCCheKob70, Author = { M.P. do~Carmo and S.S. Chern and S. Kobayashi }, Title = { {M}inimal submanifolds of a sphere with second fundamental form of constant length }, Booktitle = { {F}unct. {A}nal. {R}elated {T}opics. {P}rof. {C}onf. {H}onor of {M}arshall {S}tone. }, Publisher = { Springer }, Address = { Berlin }, Pages = { 59-75 }, Year = { 1970 } } @Incollection{ doCCol77, Author = { M.P. do~Carmo and A.G. Colares }, Title = { {O}n minimal immersions with parallel curvature tensor }, Booktitle = { {G}eometry and {T}opology }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 597 }, Pages = { 104-113 }, Series = { Lecture Notes in Math. }, Year = { 1977 } } @Unpublished{ doCDaj, Author = { M.P. do~Carmo and M. Dajczer }, Title = { {H}elicoidal surfaces with constant mean curvature }, Note = { Acad. Bras. Cien\.c. preprint } } @Article{ doCDaj83, Author = { M.P. do~Carmo and M. Dajczer }, Title = { {R}otation hypersurfaces in spaces of constant curvature }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 227 }, Pages = { 685-707 }, Year = { 1983 } } @Article{ doCLaw83, Author = { M.P. do~Carmo and H.B. Lawson }, Title = { {O}n {A}lexandrov-{B}ernstein theorems in hyperbolic space }, Journal = { Duke Math.\ J. }, Volume = { 50 }, Pages = { 995-1003 }, Year = { 1983 } } @Article{ doCPen79, Author = { M.P. do~Carmo and C.K. Peng }, Title = { {S}table complete minimal surfaces in {${\bf {R}}^3$} are planes }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 1 }, Pages = { 903-906 }, Year = { 1979 } } @Article{ doCWal70, Author = { M.P. do~Carmo and N.R. Wallach }, Title = { {R}epresentations of compact {L}ie groups and minimal immersions in spheres }, Journal = { J. Differential Geom. }, Volume = { 4 }, Pages = { 91-104 }, Year = { 1970 } } @Article{ doCWal71, Author = { M.P. do~Carmo and N.R. Wallach }, Title = { {M}inimal immersions of spheres into spheres }, Journal = { Ann.\ of Math. }, Volume = { 93 }, Pages = { 43-62 }, Year = { 1971 } } @Article{ Dra91, Author = { S. Dragomir }, Title = { {G}eneralized {H}opf manifolds, locally conformal {K}aehler structures and real hypersurfaces }, Journal = { Kodai Math.\ J. }, Volume = { 14 }, Pages = { 366-391 }, Year = { 1991 } } @Book{ DraWoo89, Author = { S. Dragomir and J.C. Wood }, Title = { {S}ottovariet{\`a} minimali ed applicazioni armoniche }, Publisher = { Pitagora }, Address = { Bologna }, Volume = { 35 }, Series = { Quad.\ Unione Mat.\ Italiana }, Year = { 1989 } } @Article{ Dua, Author = { Y.S. Duan }, Title = { {H}armonic maps and their application to general relativity }, Journal = { Phys.\ Rev.\ Lett. }, Volume = { 1984 } } @Article{ Dua84, Author = { Y.S. Duan }, Title = { {S}olution of {E}uler's equation in the theory of harmonic mappings and its applications to general relativity }, Journal = { Acta Phys.\ Sinica }, Volume = { 33 }, Pages = { 826-832 }, Year = { 1984 } } @Incollection{ Dub83, Author = { M. Dubois-Violette }, Title = { {S}tructures complexes au-dessus des vari\'et\'es }, Booktitle = { {M}ath\'ematique et {P}hysique }, Editor = { L. Boutet~de~Monvel and A. Douady and J.-L. Verdier }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 37 }, Pages = { 1-42 }, Series = { Progr.\ Math. }, Year = { 1983 } } @Unpublished{ Duc93, Author = { D.M. Duc }, Title = { {S}mooth minimizers of certain non-polynomial growth functionals }, Note = { Preprint }, Year = { 1993 } } @Article{ Duc95, Author = { D.M. Duc }, Title = { {V}ariation problems of certain functionals }, Journal = { Internat.\ J. Math. }, Volume = { 6 }, Pages = { 503-535 }, Year = { 1995 } } @Misc{ DucEel, Author = { D.M. Duc and J. Eells }, Title = { {O}n the regularity of biharmonic maps } } @Article{ DucEel91, Author = { D.M. Duc and J. Eells }, Title = { {R}egularity of exponentially harmonic functions }, Journal = { Internat.\ J. Math. }, Volume = { 2 }, Pages = { 395-408 }, Year = { 1991 } } @Misc{ DucHie, Author = { D.M. Duc and N.V. Hieu }, Title = { {G}raphs with prescribed mean curvature on hyperbolic spaces } } @Article{ DucHie95, Author = { D.M. Duc and N.V. Hieu }, Title = { {G}raphs with prescribed mean curvature on {P}oincar\'e disk }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 27 }, Pages = { 353-358 }, Year = { 1995 } } @Misc{ DucSal, Author = { D.M. Duc and I. Salavessa }, Title = { {O}n a class of quasilinear elliptic equations } } @Article{ DucSal94, Author = { D.M. Duc and I. Salavessa }, Title = { {O}n a class of graphs with prescribed mean curvature }, Journal = { Manuscripta Math. }, Volume = { 82 }, Pages = { 227-239 }, Year = { 1994 } } @Article{ Duc76, Author = { J.L. Ducourtioux }, Title = { {F}ormule de la moyenne pour les applications harmoniques }, Journal = { Bull.\ Sci.\ Math }, Volume = { 100 }, Pages = { 229-239 }, Year = { 1976 } } @Article{ Duc77, Author = { J.L. Ducourtioux }, Title = { {U}n th\'eor\`eme d'annulation non lin\'eaire }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 285 }, Pages = { 1017-1019 }, Year = { 1977 } } @Article{ Duc78, Author = { J.L. Ducourtioux }, Title = { {T}emps de vie des solutions de l'\'equation de la chaleur de {E}ells--{S}ampson }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 286 }, Pages = { 333-336 }, Year = { 1978 } } @Article{ Duh95, Author = { F. Duheille }, Title = { {S}ur l'image des morphismes harmoniques {\`a} valeurs dans {${\bf {R}}^2$} ou {${\bf {R}}^3$}. }, Journal = { C. R. Acad.\ Sci.\ Paris S\'er.\ I Math. }, Volume = { 320 }, Pages = { 1495-1500 }, Year = { 1995 } } @Article{ Duh97, Author = { F. Duheille }, Title = { {U}ne preuve probabiliste elementaire d'un resultat de {P} {B}aird et {J} {C} {W}ood }, Journal = { Ann.\ Inst.\ H. Poincar\'e Probab.\ Statist. }, Volume = { 33 }, Pages = { 283--291 }, Year = { 1997 } } @Article{ Dun92, Author = { G. Dunne }, Title = { {C}hern-{S}imons solitions, {T}oda theories and the chiral model }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 150 }, Pages = { 519-535 }, Year = { 1992 } } @Unpublished{ Duz85, Author = { F. Duzaar }, Title = { {D}ie {R}egularit\"at von {A}bbildungen zwischen {R}iemannschen {M}annigfaltigk\"aten, die das {E}nergieintegral unter einer {H}indernisbedingung minimieren }, Note = { D\"usseldorf }, Year = { 1985 } } @Article{ Duz87, Author = { F. Duzaar }, Title = { {V}ariational inequalities and harmonic mappings }, Journal = { J. Reine Angew.\ Math. }, Volume = { 374 }, Pages = { 39-60 }, Year = { 1987 } } @Article{ Duz91, Author = { F. Duzaar }, Title = { {R}egularity of {$p$}-harmonic maps into a closed hemisphere }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 5 }, Pages = { 157-170 }, Year = { 1991 } } @Article{ Duz93, Author = { F. Duzaar }, Title = { {O}n the existence of surfaces with prescribed mean curvature and boundary in higher dimensions }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 10 }, Pages = { 131-214 }, Year = { 1993 } } @Article{ DuzFuc86, Author = { F. Duzaar and M. Fuchs }, Title = { {O}ptimal regularity theorems for variational problems with obstacles }, Journal = { Manuscripta Math. }, Pages = { 209-234 }, Year = { 1986 } } @Article{ DuzFuc86A, Author = { F. Duzaar and M. Fuchs }, Title = { {V}ariational problems with non convex obstacles and an integral constraint for vector valued functions }, Journal = { Math.\ Z. }, Volume = { 191 }, Pages = { 581-591 }, Year = { 1986 } } @Article{ DuzFuc90, Author = { F. Duzaar and M. Fuchs }, Title = { {E}xistenz und {R}egularit\"at von {H}yperfl\"achen mit vorgeschrebener mittlerer {K}r\"ummung }, Journal = { Analysis }, Volume = { 10 }, Pages = { 193-230 }, Year = { 1990 } } @Article{ DuzFuc90A, Author = { F. Duzaar and M. Fuchs }, Title = { {O}n removable singularities of {$p$}-harmonic maps }, Journal = { Analyse non-lin\'eaire }, Volume = { 7 }, Pages = { 385-405 }, Year = { 1990 } } @Article{ DuzFuc91, Author = { F. Duzaar and M. Fuchs }, Title = { {E}inige {B}ermerkungen \"uber die {R}egularit\"at von {S}tation\"aren {P}unkten gewisser geometrischer {V}ariationsintegrale }, Journal = { Math.\ Nachr. }, Volume = { 152 }, Pages = { 39-47 }, Year = { 1991 } } @Article{ DuzFuc91A, Author = { F. Duzaar and M. Fuchs }, Title = { {E}xistence and regularity of functions which minimize certain energies in homotopy classes of mappings }, Journal = { Asymptotic Anal. }, Volume = { 5 }, Pages = { 129-144 }, Year = { 1991 } } @Article{ DuzGro94, Author = { F. Duzaar and J.F. Grotowski }, Title = { {E}nergy minimizing harmonic maps with an obstacle at the free boundary }, Journal = { Manuscripta Math. }, Volume = { 83 }, Pages = { 291-314 }, Year = { 1994 } } @Article{ DuzSte89, Author = { F. Duzaar and K. Steffen }, Title = { {A}n optimal estimate for the singular set of a harmonic map in the free boundary }, Journal = { J. Reine Angew.\ Math. }, Volume = { 401 }, Pages = { 157-187 }, Year = { 1989 } } @Article{ DuzSte89A, Author = { F. Duzaar and K. Steffen }, Title = { {A} partial regularity theorem for harmonic maps at a free boundary }, Journal = { Asymptotic Anal. }, Volume = { 2 }, Pages = { 299-343 }, Year = { 1989 } } @Article{ Dzi81, Author = { G. Dziuk }, Title = { \"{U}ber die {S}tetigkeit teilweise freier {M}inimalfl\"achen }, Journal = { Manuscripta Math. }, Volume = { 36 }, Pages = { 241-251 }, Year = { 1981 } } @Article{ Dzi85, Author = { G. Dziuk }, Title = { {${C}^2$}-regularity for partially free minimal surfaces }, Journal = { Math.\ Z. }, Volume = { 189 }, Pages = { 71-79 }, Year = { 1985 } } @Incollection{ EarEel69, Author = { C.J. Earle and J. Eells }, Title = { {D}eformation of {R}iemann surfaces }, Booktitle = { {L}ectures in {M}odern {A}nalysis and its {A}pplications }, Editor = { C.T. Taam }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 103 }, Pages = { 122-149 }, Series = { Lecture Notes in Math. }, Year = { 1969 } } @Article{ EarEel69A, Author = { C.J. Earle and J. Eells }, Title = { {A} fibre bundle description of {T}eichm\"uller theory }, Journal = { J. Differential Geom. }, Volume = { 3 }, Pages = { 19-43 }, Year = { 1969 } } @Article{ EarRos, Author = { R. Earp and H. Rosenberg }, Title = { {T}he {D}irichlet problem for the minimal surface equation on unbounded planar domains }, Journal = { J. Math.\ Pures Appl. } } @Misc{ EarRosA, Author = { R. Earp and H. Rosenberg }, Title = { {O}n the values of the {G}auss map of complete minimal surfaces in {${\bf {R}}^3$} } } @Article{ Eas84, Author = { M.G. Eastwood }, Title = { {C}omplexification, twistor theory, and harmonic maps from {R}iemann surfaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 11 }, Pages = { 317-328 }, Year = { 1984 } } @Article{ Ebe73, Author = { P. Eberlein }, Title = { {W}hen is a geodesic flow of {A}nosov type? {I}{I} }, Journal = { J. Differential Geom. }, Volume = { 8 }, Pages = { 565-577 }, Year = { 1973 } } @Article{ Eck82, Author = { K. Ecker }, Title = { {E}stimates for evolutionary surfaces of prescribed mean curvature }, Journal = { Math.\ Z. }, Volume = { 180 }, Pages = { 179-192 }, Year = { 1982 } } @Article{ Eck95, Author = { K. Ecker }, Title = { {O}n regularity for mean curvature flow of hypersurfaces }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 31 }, Pages = { 107-126 }, Year = { 1995 } } @Article{ EckHui89, Author = { K. Ecker and G. Huisken }, Title = { {M}ean curvature evolution of entire graphs }, Journal = { Ann.\ of Math. }, Volume = { 130 }, Pages = { 453-471 }, Year = { 1989 } } @Article{ EckHui90, Author = { K. Ecker and G. Huisken }, Title = { {A} {B}ernstein result for minimal graphs of controlled growth }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 397-400 }, Year = { 1990 } } @Article{ Eco93, Author = { M. Economakis }, Title = { {A} counterexample to uniqueness and regularity for harmonic maps between hyperbolic spaces }, Journal = { J. Geom.\ Anal. }, Volume = { 3 }, Pages = { 27-36 }, Year = { 1993 } } @Article{ Edm79, Author = { A.L. Edmonds }, Title = { {D}eformation of maps to branched coverings in dimension two }, Journal = { Ann.\ of Math. }, Volume = { 110 }, Pages = { 113-125 }, Year = { 1979 } } @Incollection{ Eel72, Author = { J. Eells }, Title = { {F}ibring spaces of maps }, Booktitle = { {S}ymposium on {I}nfinite {D}imensional {T}opology (1967) }, Editor = { R.D. Anderson }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 69 }, Pages = { 43-57 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1972 } } @Incollection{ Eel76, Author = { J. Eells }, Title = { {E}lliptic operators on manifolds }, Booktitle = { {G}lobal {A}nalysis and its {A}pplications, {I} }, Publisher = { I.C.T.P. }, Address = { Trieste }, Pages = { 95-152 }, Year = { 1976 } } @Incollection{ Eel77, Author = { J. Eells }, Title = { {H}armonic maps of surfaces }, Booktitle = { {E}ighth {A}nn. {N}at. {M}ath. {C}onf. ({T}erhan) }, Pages = { 157-163 }, Year = { 1977 } } @Incollection{ Eel78, Author = { J. Eells }, Title = { {O}n the surfaces of {D}elaunay and their {G}auss maps }, Booktitle = { {P}roc. {I}{V} {I}nternational {C}olloquium on {D}ifferential {G}eometry {S}antiago de {C}ompostela }, Pages = { 97-116 }, Year = { 1978 } } @Article{ Eel79, Author = { J. Eells }, Title = { {M}inimal graphs }, Journal = { Manuscripta Math. }, Volume = { 28 }, Pages = { 101-108 }, Year = { 1979 } } @Incollection{ Eel80, Author = { J. Eells }, Title = { {E}xamples of harmonic and holomorphic maps }, Booktitle = { {A}nalytic {F}unctions, {K}ozubnik 1979 }, Editor = { J. {\L}awrynowicz }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 798 }, Pages = { 155-160 }, Series = { Lecture Notes in Math. }, Year = { 1980 } } @Incollection{ Eel83, Author = { J. Eells }, Title = { {V}ariational theory in fibre bundles: examples }, Booktitle = { {D}ifferential {G}eometry and {M}athematical {P}hysics }, Editor = { M. Cahen and M. de~Wilde and L. Lemaire and L. Vanhecke }, Publisher = { Reidel }, Address = { Dortrecht, Holland, London }, Volume = { 3 }, Pages = { 149-158 }, Series = { Math.\ Phys.\ Stud. }, Year = { 1983 } } @Incollection{ Eel84, Author = { J. Eells }, Title = { {G}auss maps of surfaces }, Booktitle = { {P}erspectives in {M}ath. ({O}berwolfach 1944-1984) }, Publisher = { Birkh\"auser }, Pages = { 111-129 }, Year = { 1984 } } @Incollection{ Eel84A, Author = { J. Eells }, Title = { {O}n equivariant harmonic maps }, Booktitle = { {P}roc. {S}econd {C}onference {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei 1981 }, Publisher = { Sci.\ Press }, Address = { Beijing }, Pages = { 55-73 }, Year = { 1984 } } @Incollection{ Eel84B, Author = { J. Eells }, Title = { {R}egularity of certain harmonic maps }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 137-147 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Incollection{ Eel85, Author = { J. Eells }, Title = { {C}ertain variational principles in {R}iemannian geometry }, Booktitle = { {D}ifferential {G}eometry }, Editor = { L.A. Cordero }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 131 }, Pages = { 46-60 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Incollection{ Eel85A, Author = { J. Eells }, Title = { {M}inimal branched immersions into three-manifolds }, Booktitle = { {G}eometry and {T}opology }, Editor = { J.C. Alexander and J.L. Harer }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1167 }, Pages = { 81-94 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Unpublished{ Eel87, Author = { J. Eells }, Title = { {H}armonic maps between spheres }, Note = { Third World Academy of Sciences Lecture. Nankai Institute, Tianjin, China }, Year = { 1987 } } @Unpublished{ Eel87A, Author = { J. Eells }, Title = { {O}n deformations of closed {R}iemann surfaces }, Note = { Third World Academy of Sciences Lecture, I.M.P.A., Rio de Janeiro }, Year = { 1987 } } @Article{ Eel87B, Author = { J. Eells }, Title = { {T}he surfaces of {D}elaunay }, Journal = { Math.\ Intelligencer }, Volume = { 9 }, Pages = { 53-57 }, Year = { 1987 } } @Book{ Eel92, Author = { J. Eells }, Title = { {H}armonic maps, {S}elected papers of {J}ames {E}ells and collaborators }, Publisher = { World Sci.\ Publ. }, Address = { Singapore }, Year = { 1992 } } @Article{ EelFer91, Author = { J. Eells and M.J. Ferreira }, Title = { {O}n representing homotopy classes by harmonic maps }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 23 }, Pages = { 160-162 }, Year = { 1991 } } @Article{ EelLem78, Author = { J. Eells and L. Lemaire }, Title = { {A} report on harmonic maps }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 10 }, Pages = { 1-68 }, Year = { 1978 } } @Article{ EelLem80, Author = { J. Eells and L. Lemaire }, Title = { {O}n the construction of harmonic and holomorphic maps between surfaces }, Journal = { Math.\ Ann. }, Volume = { 252 }, Pages = { 27-52 }, Year = { 1980 } } @Incollection{ EelLem81, Author = { J. Eells and L. Lemaire }, Title = { {D}eformations of metrics and associated harmonic maps }, Booktitle = { {G}eometry and {A}nalysis, {P}atodi {M}emorial {V}ol. }, Publisher = { Tata Inst. }, Address = { Bombay }, Pages = { 33-45 }, Year = { 1981 } } @Book{ EelLem83, Author = { J. Eells and L. Lemaire }, Title = { {S}elected topics in harmonic maps }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 50 }, Series = { CBMS Regional Conf.\ Ser.\ in Math. }, Year = { 1983 } } @Article{ EelLem84, Author = { J. Eells and L. Lemaire }, Title = { {E}xamples of harmonic maps from disks to hemispheres }, Journal = { Math.\ Z. }, Volume = { 185 }, Pages = { 517-519 }, Year = { 1984 } } @Article{ EelLem88, Author = { J. Eells and L. Lemaire }, Title = { {A}nother report on harmonic maps }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 20 }, Pages = { 385-524 }, Year = { 1988 } } @Article{ EelLem92, Author = { J. Eells and L. Lemaire }, Title = { {S}ome properties of exponentially harmonic maps }, Journal = { Banach Center Publ. }, Volume = { 27 }, Pages = { 129-136 }, Year = { 1992 } } @Article{ EelPol84, Author = { J. Eells and J.C. Polking }, Title = { {R}emovable singularities of harmonic maps }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 33 }, Pages = { 859-871 }, Year = { 1984 } } @Article{ EelRat90, Author = { J. Eells and A. Ratto }, Title = { {H}armonic maps between spheres and ellipsoids }, Journal = { Internat.\ J. Math. }, Volume = { 1 }, Pages = { 1-27 }, Year = { 1990 } } @Book{ EelRat93, Author = { J. Eells and A. Ratto }, Title = { {H}armonic maps and minimal immersions with symmetries }, Publisher = { Princeton University Press }, Volume = { 130 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1993 } } @Article{ EelSal83, Author = { J. Eells and S.M. Salamon }, Title = { {C}onstructions twistorielles des applications harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 296 }, Pages = { 685-687 }, Year = { 1983 } } @Article{ EelSal85, Author = { J. Eells and S.M. Salamon }, Title = { {T}wistorial construction of harmonic maps of surfaces into four-manifolds }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 12 }, Pages = { 589-640 }, Year = { 1985 } } @Article{ EelSam64, Author = { J. Eells and J.H. Sampson }, Title = { {E}nergie et d\'eformations en g\'eom\'etrie diff\'erentielle }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 14 }, Pages = { 61-69 }, Year = { 1964 } } @Article{ EelSam64A, Author = { J. Eells and J.H. Sampson }, Title = { {H}armonic mappings of {R}iemannian manifolds }, Journal = { Amer.\ J. Math. }, Volume = { 86 }, Pages = { 109-160 }, Year = { 1964 } } @Incollection{ EelSam65, Author = { J. Eells and J.H. Sampson }, Title = { {V}ariational theory in fibre bundles }, Booktitle = { {P}roc. {U}.{S}.--{J}apan {S}eminar on {D}ifferential {G}eometry {K}yoto }, Pages = { 22-33 }, Year = { 1965 } } @Article{ EelWoo76, Author = { J. Eells and J.C. Wood }, Title = { {R}estrictions on harmonic maps of surfaces }, Journal = { Topology }, Volume = { 15 }, Pages = { 263-266 }, Year = { 1976 } } @Article{ EelWoo81, Author = { J. Eells and J.C. Wood }, Title = { {M}aps of minimum energy }, Journal = { J. London Math.\ Soc. }, Volume = { 23 }, Pages = { 303-310 }, Year = { 1981 } } @Article{ EelWoo82, Author = { J. Eells and J.C. Wood }, Title = { {T}he existence and construction of certain harmonic maps }, Journal = { Sympos.\ Math. }, Volume = { 26 }, Pages = { 123-138 }, Year = { 1982 } } @Article{ EelWoo83, Author = { J. Eells and J.C. Wood }, Title = { {H}armonic maps from surfaces to complex projective spaces }, Journal = { Adv.\ in Math. }, Volume = { 49 }, Pages = { 217-263 }, Year = { 1983 } } @Article{ EelYiu95, Author = { J. Eells and P. Yiu }, Title = { {P}olynomial harmonic morphisms between {E}uclidean spheres }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 123 }, Pages = { 2921-2925 }, Year = { 1995 } } @Article{ EicFor79, Author = { H. Eichenherr and M. Forger }, Title = { {O}n the dual symmetry of the nonlinear {$\sigma$}-models }, Journal = { Nuclear Phys.\ B }, Volume = { 155 }, Pages = { 381-393 }, Year = { 1979 } } @Article{ EicFor80, Author = { H. Eichenherr and M. Forger }, Title = { {M}ore about nonlinear sigma models on symmetric spaces }, Journal = { Nuclear Phys.\ B }, Volume = { 1644 }, Pages = { 528-535 }, Year = { 1980 } } @Article{ EicFor81, Author = { H. Eichenherr and M. Forger }, Title = { {H}igher local conservation laws for nonlinear {$\sigma$}-models on symmetric spaces }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 82 }, Pages = { 227-255 }, Year = { 1981 } } @Article{ EicFor87, Author = { H. Eichenherr and M. Forger }, Title = { {M}ore about nonlinear sigma models on symmetric spaces (correction) }, Journal = { Nuclear Phys.\ B }, Volume = { 282 }, Pages = { 745-746 }, Year = { 1987 } } @Unpublished{ Eji, Author = { N. Ejiri }, Title = { {T}he boundary of the space of full harmonic maps of {${S}^2$} into {${S}^{2m}(1)$} and extra eigenfunctions }, Note = { Preprint } } @Misc{ EjiA, Author = { N. Ejiri }, Title = { {A} {G}auss parametrization of minimal surface in {${R}^{N}$} } } @Unpublished{ EjiB, Author = { N. Ejiri }, Title = { {S}ome minimal immersions of spheres into a unit sphere }, Note = { Preprint } } @Article{ Eji79, Author = { N. Ejiri }, Title = { {C}ompact minimal submanifolds of a sphere with positive {R}icci curvature }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 31 }, Pages = { 251-256 }, Year = { 1979 } } @Article{ Eji81, Author = { N. Ejiri }, Title = { {T}otally real submanifolds in a {$6$}-sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 83 }, Pages = { 759-763 }, Year = { 1981 } } @Article{ Eji82, Author = { N. Ejiri }, Title = { {A} counter-example for {W}einer's open question }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 31 }, Pages = { 209-211 }, Year = { 1982 } } @Article{ Eji83, Author = { N. Ejiri }, Title = { {T}he index of minimal immersions of {${S}^2$} into {${S}^{2n}$} }, Journal = { Math.\ Z. }, Volume = { 184 }, Pages = { 127-132 }, Year = { 1983 } } @Article{ Eji86, Author = { N. Ejiri }, Title = { {C}alabi lifting and surface geometry in {${S}^4$} }, Journal = { Tokyo J. Math. }, Volume = { 9 }, Pages = { 297-324 }, Year = { 1986 } } @Article{ Eji86A, Author = { N. Ejiri }, Title = { {E}quivariant minimal immersions of {${S}^2$} in {${S}^{2m}(1)$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 297 }, Pages = { 105-124 }, Year = { 1986 } } @Article{ Eji88, Author = { N. Ejiri }, Title = { {I}sotropic harmonic maps of {R}iemann surfaces into the de~{S}itter space time }, Journal = { Quart.\ J. Math.\ Oxford }, Volume = { 39 }, Pages = { 291-306 }, Year = { 1988 } } @Article{ Eji88A, Author = { N. Ejiri }, Title = { {W}illmore surfaces with a duality in {${S}^{N}(1)$} }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 57 }, Pages = { 383-416 }, Year = { 1988 } } @Article{ Eji91, Author = { N. Ejiri }, Title = { {T}wo applications of the unit normal bundle of a minimal surface in {${\bf {R}}^{N}$} }, Journal = { Pacific J. Math. }, Volume = { 147 }, Pages = { 291-300 }, Year = { 1991 } } @Article{ Eji94, Author = { N. Ejiri }, Title = { {M}inimal deformation of a non-full minimal surface in {${S}^{4}(1)$} }, Journal = { Compositio Math. }, Volume = { 90 }, Pages = { 183-209 }, Year = { 1994 } } @Misc{ EjiKot, Author = { N. Ejiri and M. Kotani }, Title = { {E}igenfunctions with eigenvalue {$2$} for {L}aplacian of minimal surfaces of genus {$0$} in {${S}^{2n}(1)$} } } @Article{ EjiKot92, Author = { N. Ejiri and M. Kotani }, Title = { {M}inimal surfaces in {${S}^{2m}(1)$} with extra eigenfunctions }, Journal = { Quart.\ J. Math.\ Oxford }, Volume = { 43 }, Pages = { 421-440 }, Year = { 1992 } } @Article{ EjiKot93, Author = { N. Ejiri and M. Kotani }, Title = { {I}ndex and flat ends of minimal surfaces }, Journal = { Tokyo J. Math. }, Volume = { 16 }, Pages = { 37-48 }, Year = { 1993 } } @Misc{ EjiMic, Author = { N. Ejiri and M. Micallef }, Title = { {C}omparison of second variation of area and second variation of energy for minimal surfaces } } @Misc{ EjiMicA, Author = { N. Ejiri and M. Micallef }, Title = { {S}urfaces of constant mean curvature in negatively curved 3-manifolds } } @Article{ ElSMouZai94, Author = { M.F. El-Sadbagh and M.F. Mourad and R.A. Zait }, Title = { {S}tatic solitons in the {${\bf {C}}{P}^2$} sigma model }, Journal = { Phys.\ Scripta }, Volume = { 50 }, Pages = { 321-325 }, Year = { 1994 } } @Article{ ElS92, Author = { H.K. El-Sayed }, Title = { {O}n rigidity of harmonic mappings into elliptic space }, Journal = { J. Inst.\ Math.\ Comput.\ Sci.\ Math.\ Ser. }, Volume = { 5 }, Pages = { 307-314 }, Year = { 1992 } } @Unpublished{ Eli, Author = { H.I. Eliasson }, Title = { {A} priori local growth estimates for mappings }, Note = { preprint } } @Article{ Eli67, Author = { H.I. Eliasson }, Title = { {G}eometry of manifolds of maps }, Journal = { J. Differential Geom. }, Volume = { 1 }, Pages = { 169-194 }, Year = { 1967 } } @Incollection{ Eli70, Author = { H.I. Eliasson }, Title = { {V}ariational integrals in fiber bundles }, Booktitle = { {G}lobal {A}nalysis }, Editor = { S.S. Chern and S. Smale }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 16 }, Pages = { 67-89 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1970 } } @Incollection{ Eli74, Author = { H.I. Eliasson }, Title = { {I}ntroduction to global calculus of variations }, Booktitle = { {G}lobal {A}nalysis and {I}ts {A}pplications, {V}ol {I}{I} }, Publisher = { I.C.T.P. }, Address = { Trieste }, Pages = { 113-135 }, Year = { 1974 } } @Incollection{ Eli85, Author = { H.I. Eliasson }, Title = { {A} priori growth and {H}\"older estimates for harmonic mappings }, Booktitle = { {D}ifferential {G}eometry, {C}alculus of {V}ariations and their {A}pplications }, Publisher = { M. Dekker }, Address = { New York }, Volume = { 100 }, Pages = { 177-209 }, Series = { Lecture Notes in Pure and Appl.\ Math. }, Year = { 1985 } } @Incollection{ Elw88, Author = { K.D. Elworthy }, Title = { {B}rownian motion and harmonic forms }, Booktitle = { {S}tochastic analysis and related topics }, Editor = { H. Korezlioglu and A.S. Ustenel }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1316 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Incollection{ ElwKen86, Author = { K.D. Elworthy and W.S. Kendall }, Title = { {F}actorization of harmonic maps and {B}rownian motions }, Booktitle = { {F}rom local times to global geometry, control and physics }, Editor = { K.D. Elworthy }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 150 }, Pages = { 75-83 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1986 } } @Unpublished{ ElwRos95, Author = { K.D. Elworthy and S. Rosenberg }, Title = { {H}omotopy and homology vanishing theorems and the stability of stochastic flows }, Note = { Preprint }, Year = { 1995 } } @Article{ ElKGal96, Author = { A. El~Kacimi~Alaoui and E. Gallego~Gomez }, Title = { {A}pplications harmoniques feuillet\'ees }, Journal = { Illinois J. Math. }, Volume = { 40 }, Pages = { 115-122 }, Year = { 1996 } } @Incollection{ ElS87, Author = { A. El~Soufi }, Title = { {I}mmersions minimales sph\'eriques: {R}estrictions sur la courbure et la codimension }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 255-266 }, Series = { Ast\'erisque }, Year = { 1987 } } @Unpublished{ ElS90, Author = { A. El~Soufi }, Title = { {I}mmersions minimales et applications harmoniques d'une vari\'et\'e compacte dans les sph\`eres }, Note = { Tours }, Year = { 1990 } } @Unpublished{ ElS91, Author = { A. El~Soufi }, Title = { {G}\'eom\'etrie des sous-vari\'et\'es admettant une structure k\"ahlerienne ou un second nombre de {B}etti non nul }, Note = { Preprint, Univ. Tours }, Year = { 1991 } } @Unpublished{ ElS92A, Author = { A. El~Soufi }, Title = { {I}ndice de {M}orse des applications harmoniques de la sph\`ere }, Note = { Preprint, Univ. Tours }, Year = { 1992 } } @Article{ ElS93, Author = { A. El~Soufi }, Title = { {A}pplications harmoniques, immersions minimales et transformations conformes de la sph\`ere }, Journal = { Compositio Math. }, Volume = { 85 }, Pages = { 281-298 }, Year = { 1993 } } @Article{ ElSIli86, Author = { A. El~Soufi and S. Ilias }, Title = { {I}mmersions minimales, premiere valeur propre du laplacien et volume conforme }, Journal = { Math.\ Ann. }, Volume = { 275 }, Pages = { 257--267 }, Year = { 1986 } } @Article{ ElSIli92, Author = { A. El~Soufi and S. Ilias }, Title = { {U}ne inegalit\'e du type ``{R}eilly'' pour les sous-vari\'et\'es de l'espace hyperbolique }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 67 }, Pages = { 167-181 }, Year = { 1992 } } @Article{ ElSJeu92, Author = { A. El~Soufi and A. Jeune }, Title = { {I}ndice de {M}orse des applications {$p$}-harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 315 }, Pages = { 1189-1192 }, Year = { 1992 } } @Article{ ElSJeu96, Author = { A. El~Soufi and A. Jeune }, Title = { {I}ndice de {M}orse des applications {$p$}-harmoniques }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 13 }, Pages = { 229-250 }, Year = { 1996 } } @Article{ Eps75, Author = { D.B.A. Epstein }, Title = { {N}atural tensor on {R}iemannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 10 }, Pages = { 631-645 }, Year = { 1975 } } @Article{ Erb72, Author = { J.A. Erbacher }, Title = { {I}sometric immersions with constant mean curvature and triviality of the normal bundle }, Journal = { Nagoya Math.\ J. }, Volume = { 45 }, Pages = { 139-165 }, Year = { 1972 } } @Unpublished{ ErcKnoTru91, Author = { N. Ercolani and H. Kn{\"o}rrer and E. Trubowitz }, Title = { {H}yperelliptic curves that generate constant mean curvature tori in {${\bf {R}}^3$} }, Note = { Preprint, ETH }, Year = { 1991 } } @Unpublished{ Erd, Author = { S. Erdem }, Title = { {H}armonic maps as a solution of wave equation and quadratic differentials }, Note = { Preprint } } @Article{ Erd82, Author = { S. Erdem }, Title = { {H}armonic maps into real hyperbolic space }, Journal = { J. Univ.\ Lecce }, Year = { 1982 } } @Article{ Erd83, Author = { S. Erdem }, Title = { {H}armonic maps from surfaces into pseudo-{R}iemannian spheres and hyperbolic spaces }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 94 }, Pages = { 483-494 }, Year = { 1983 } } @Unpublished{ Erd84, Author = { S. Erdem }, Title = { {O}n the classification of harmonic maps of {R}iemann surfaces into some homogeneous spaces }, Note = { Leeds Ph.D. Thesis }, Year = { 1984 } } @Article{ Erd97, Author = { S. Erdem }, Title = { {H}armonic maps of {L}orentz surfaces, quadratic differentials and paraholomorphicity }, Journal = { Beitr{\"a}ge Algebra Geom. }, Volume = { 38 }, Pages = { 19--32 }, Year = { 1997 } } @Article{ ErdGla83, Author = { S. Erdem and J.F. Glazebrook }, Title = { {H}armonic maps of {R}iemann surfaces to indefinite complex hyperbolic and projective spaces }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 47 }, Pages = { 547-562 }, Year = { 1983 } } @Article{ ErdWoo83, Author = { S. Erdem and J.C. Wood }, Title = { {O}n the construction of harmonic maps into a {G}rassmannian }, Journal = { J. London Math.\ Soc. }, Volume = { 28 }, Pages = { 161-174 }, Year = { 1983 } } @Incollection{ Eri76, Author = { J.L. Ericksen }, Title = { {E}quilibrium theory of liquid crystals }, Booktitle = { {A}dv. {L}iquid. {C}ryst. }, Publisher = { Academic Press }, Volume = { 2 }, Pages = { 233-298 }, Year = { 1976 } } @Article{ Eri77, Author = { A. Eris }, Title = { {F}urther applications of harmonic mappings of {R}iemannian manifolds to gravitational fields }, Journal = { Math.\ Phys. }, Volume = { 18 }, Pages = { 824-829 }, Year = { 1977 } } @Article{ EriNut75, Author = { A. Eris and Y. Nutku }, Title = { {H}armonic mappings of {R}iemannian manifolds and stationary vacuum space-time with whole cylinder symmetry }, Journal = { Math.\ Phys. }, Volume = { 16 }, Pages = { 1431-1434 }, Year = { 1975 } } @Article{ Ere84, Author = { E.A. Er{\"e}min }, Title = { {S}tability of harmonic mappings of 3 dimensional domains }, Journal = { Dinamika Sploshn.\ Sredy }, Volume = { 59 }, Pages = { 73-100 }, Year = { 1984 } } @Article{ EscGuaTri85, Author = { J.-H. Eschenburg and I.V. Guadalupe and R. Tribuzy }, Title = { {T}he fundamental equations of minimal surfaces in {${\bf {C}}{P}^{2}$} }, Journal = { Math.\ Ann. }, Volume = { 270 }, Pages = { 571-598 }, Year = { 1985 } } @Misc{ EscTri, Author = { J.-H. Eschenburg and R. Tribuzy }, Title = { {$(2,0)$}-geodesic immersions of {K}{\"a}hler manifolds } } @Article{ EscTri88, Author = { J.-H. Eschenburg and R. Tribuzy }, Title = { {B}ranch points of conformal mappings of surfaces }, Journal = { Math.\ Ann. }, Volume = { 279 }, Pages = { 621-633 }, Year = { 1988 } } @Incollection{ EscTri91, Author = { J.-H. Eschenburg and R. Tribuzy }, Title = { {C}onformal mappings of surfaces and {C}auchy-{R}iemann inequalities }, Booktitle = { {D}ifferential {G}eometry }, Publisher = { Longman Sci. }, Address = { Harlow }, Volume = { 52 }, Pages = { 149-170 }, Series = { Pitman Monographs Surveys Pure Appl.\ Math. }, Year = { 1991 } } @Article{ EscTri95, Author = { J.-H. Eschenburg and R. Tribuzy }, Title = { {$(1,1)$}-geodesic maps into {G}rassmann manifolds }, Journal = { Math.\ Z. }, Volume = { 220 }, Pages = { 337-346 }, Year = { 1995 } } @Unpublished{ EscTriA, Author = { J.H. Eschenburg and R. Tribuzy }, Title = { {A}ssociated families of pluriharmonic maps and isotropy }, Note = { preprint } } @Article{ Esc75, Author = { R.H. Escobales }, Title = { {R}iemannian submersions with totally geodesic fibers }, Journal = { J. Differential Geom. }, Volume = { 10 }, Pages = { 253-276 }, Year = { 1975 } } @Article{ Esc78, Author = { R.H. Escobales }, Title = { {R}iemannian submersions from complex projective space }, Journal = { J. Differential Geom. }, Volume = { 13 }, Pages = { 93-107 }, Year = { 1978 } } @Article{ EscFreMin93, Author = { J.F. Escobar and A. Freire and M. Min-Oo }, Title = { {${L}^2$} vanishing theorems in positive curvature }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 42 }, Pages = { 1545-1554 }, Year = { 1993 } } @Misc{ EstRom, Author = { F.J.M. Estudillo and A. Romero }, Title = { {G}eneralized maximal surfaces in {L}orentz-{M}inkowski space {${L}^3$} } } @Article{ Eva91, Author = { L.C. Evans }, Title = { {P}artial regularity for stationary harmonic maps into spheres }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 116 }, Pages = { 101-113 }, Year = { 1991 } } @Article{ EvaGar87, Author = { L.C. Evans and R.F. Gariepy }, Title = { {C}ompactness and partial regularity in the calculus of variations }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 36 }, Pages = { 361-371 }, Year = { 1987 } } @Article{ EvaSpr91, Author = { L.C. Evans and J. Spruck }, Title = { {M}otion of level sets by mean curvature {I} }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 635-681 }, Year = { 1991 } } @Article{ EvaSpr92, Author = { L.C. Evans and J. Spruck }, Title = { {M}otion of level sets by mean curvature {I}{I} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Pages = { 321-332 }, Year = { 1992 } } @Article{ EvaSpr92A, Author = { L.C. Evans and J. Spruck }, Title = { {M}otion of level sets by mean curvature {I}{I}{I} }, Journal = { J. Geom.\ Anal. }, Volume = { 2 }, Pages = { 121-150 }, Year = { 1992 } } @Article{ EvaSpr95, Author = { L.C. Evans and J. Spruck }, Title = { {M}otion of level sets by mean curvature {I}{V} }, Journal = { J. Geom.\ Anal. }, Volume = { 5 }, Pages = { 77-114 }, Year = { 1995 } } @Misc{ FanMee, Author = { Y. Fang and W.H. Meeks }, Title = { {T}he geometry of minimal surfaces in a halfspace in {${\bf {R}}^3$} } } @Article{ FanMee91, Author = { Y. Fang and W.H. Meeks }, Title = { {S}ome global properties of complete minimal surfaces of finite topology in {${\bf {R}}^3$} }, Journal = { Topology }, Volume = { 30 }, Pages = { 9-20 }, Year = { 1991 } } @Misc{ Far, Author = { A. Fardoun }, Title = { {S}tabilit{\'e} pour la {$p$}-{\'e}nergie de l'application {\'e}quateur de la boule dans l'ellipso\"\i de } } @Misc{ FarA, Author = { A. Fardoun }, Title = { {S}ur le probl{\`e}me de {D}irichlet pour les applications {$p$}-harmoniques de la boule dans l'ellipso\"\i de } } @Article{ FarRat97, Author = { A. Fardoun and A. Ratto }, Title = { {H}armonic maps with potential }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 5 }, Pages = { 183--197 }, Year = { 1997 } } @Article{ FarJon89, Author = { F.T. Farrell and L.E. Jones }, Title = { {N}egatively curved manifolds with exotic smooth structures }, Journal = { J. Amer.\ Math.\ Soc. }, Volume = { 2 }, Pages = { 899-908 }, Year = { 1989 } } @Article{ FarJon94, Author = { F.T. Farrell and L.E. Jones }, Title = { {C}omplex hyperbolic manifolds and exotic smooth structures }, Journal = { Invent.\ Math. }, Volume = { 117 }, Pages = { 57-74 }, Year = { 1994 } } @Article{ FarJon96, Author = { F.T. Farrell and L.E. Jones }, Title = { {S}ome non-homeomorphic harmonic homotopy equivalences }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 28 }, Pages = { 177-182 }, Year = { 1996 } } @Misc{ Fel, Author = { M. Feldman }, Title = { {P}artial regularity for harmonic maps of evolution into spheres } } @Article{ Fer93, Author = { C.J. Ferraris }, Title = { {A} class of minimal submanifolds in a 2-step nilpotent {L}ie group }, Journal = { Rev.\ Un.\ Mat.\ Argentina }, Volume = { 38 }, Pages = { 210-218 }, Year = { 1993 } } @Article{ Fer92, Author = { C. Ferreira }, Title = { {A} {G}auss-like map associated to a surface in {${\bf {R}}^3$} }, Journal = { Math.\ Z. }, Volume = { 209 }, Pages = { 363-373 }, Year = { 1992 } } @Article{ Fer84, Author = { M.J. Ferreira }, Title = { {M}orse indices for certain harmonic maps of surfaces }, Journal = { Bull.\ Soc.\ Math.\ Belg. }, Volume = { 36 }, Pages = { 131-153 }, Year = { 1984 } } @Unpublished{ Fer85, Author = { M.J. Ferreira }, Title = { {A}plica{\c c}o\~es ramificadas conformes de superf\'icies de {R}iemann e problemas variacionais }, Note = { Lisbon Thesis }, Year = { 1985 } } @Article{ Fer87, Author = { M.J. Ferreira }, Title = { {A} twistorial characterization of conformal branched immersions with parallel mean curvature }, Journal = { Bull.\ Soc.\ Math.\ Belg.\ S\'er.\ B }, Volume = { 39 }, Pages = { 47-81 }, Year = { 1987 } } @Article{ Fer93A, Author = { M.J. Ferreira }, Title = { {A} characterization of {J}acobi fields along harmonic maps }, Journal = { Internat.\ J. Math. }, Volume = { 4 }, Pages = { 545-550 }, Year = { 1993 } } @Article{ FerRigTri, Author = { M.J. Ferreira and M. Rigoli and R. Tribuzy }, Title = { {I}sometric immersions of {K}\"ahler manifolds }, Journal = { Bull.\ Soc.\ Math.\ Belg. } } @Misc{ FerTri, Author = { M.J. Ferreira and R. Tribuzy }, Title = { {O}n the type decomposition of the second fundamental form of a {K}{\"a}hler submanifold } } @Article{ FerTri93, Author = { M.J. Ferreira and R. Tribuzy }, Title = { {K}\"ahlerian submanifolds of {${\bf {R}}^n$} with plurisubharmonic {G}auss map }, Journal = { Bull.\ Soc.\ Math.\ Belg. }, Volume = { 45 }, Pages = { 183-197 }, Year = { 1993 } } @Article{ Fer70, Author = { D. Ferus }, Title = { {O}n the type number of hypersurfaces in spaces of constant curvature }, Journal = { Math.\ Ann. }, Volume = { 187 }, Pages = { 310-316 }, Year = { 1970 } } @Article{ Fer70A, Author = { D. Ferus }, Title = { {T}otally geodesic foliations }, Journal = { Math.\ Ann. }, Volume = { 188 }, Pages = { 313-316 }, Year = { 1970 } } @Article{ Fer75, Author = { D. Ferus }, Title = { {I}sometric immersions of constant curvature manifolds }, Journal = { Math.\ Ann. }, Volume = { 217 }, Pages = { 155-156 }, Year = { 1975 } } @Unpublished{ Fer80, Author = { D. Ferus }, Title = { {N}otes on isoparametric hypersurfaces }, Note = { Univ. Estadual de Campinas. Brazil }, Year = { 1980 } } @Incollection{ Fer93B, Author = { D. Ferus }, Title = { {S}urface theory, harmonic maps, and commuting {H}amiltonian flows }, Booktitle = { {D}ifferential geometry and topology ({A}lgebra, 1992) }, Publisher = { World Scientific }, Address = { River Edge }, Pages = { 71-89 }, Year = { 1993 } } @Article{ FerKar85, Author = { D. Ferus and H. Karcher }, Title = { {N}on-rotational minimal spheres and minimal cones }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 60 }, Pages = { 247-269 }, Year = { 1985 } } @Article{ FerKar85A, Author = { D. Ferus and H. Karcher }, Title = { {N}on-rotational minimal spheres and minimizing cones }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 60 }, Pages = { 247-269 }, Year = { 1985 } } @Article{ FerKarMun81, Author = { D. Ferus and H. Karcher and H.F. M{\"u}nzner }, Title = { {C}liffordalgebren und neue isoparametrische {H}yperfl\"achen }, Journal = { Math.\ Z. }, Volume = { 177 }, Pages = { 479-502 }, Year = { 1981 } } @Misc{ FerPed, Author = { D. Ferus and F. Pedit }, Title = { {C}urved flats } } @Article{ FerPedA, Author = { D. Ferus and F. Pedit }, Title = { {I}sometric immersions of space forms and soliton theory }, Journal = { Math.\ Ann. } } @Article{ FerPed90, Author = { D. Ferus and F. Pedit }, Title = { {${S}^1$}-equivariant minimal tori in {${S}^4$} and {${S}^1$}-equivariant {W}illmore tori in {${S}^3$} }, Journal = { Math.\ Z. }, Volume = { 204 }, Pages = { 269-282 }, Year = { 1990 } } @Article{ FerPedPin92, Author = { D. Ferus and F. Pedit and U. Pinkall and I. Sterling }, Title = { {M}inimal tori in {${S}^4$} }, Journal = { J. Reine Angew.\ Math. }, Volume = { 429 }, Pages = { 1-47 }, Year = { 1992 } } @Article{ FerPin89, Author = { D. Ferus and U. Pinkall }, Title = { {C}onstant curvature {$2$}-spheres in the {$4$}-sphere }, Journal = { Math.\ Z. }, Volume = { 500 }, Pages = { 265-271 }, Year = { 1989 } } @Article{ FerPinTim94, Author = { D. Ferus and U. Pinkall and M. Timmreck }, Title = { {C}onstant mean curvature planes with inner rotational symmetry in {E}uclidean 3-space }, Journal = { Math.\ Z. }, Volume = { 215 }, Pages = { 561-568 }, Year = { 1994 } } @Misc{ Fie, Author = { T. Fiedler }, Title = { {A} characteristic class for totally real surfaces in the {G}rassmannian of two planes in four-space } } @Article{ Fie85, Author = { T. Fiedler }, Title = { {E}xceptional points on surfaces in four-spaces }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 3 }, Pages = { 219-231 }, Year = { 1985 } } @Article{ Fie88, Author = { T. Fiedler }, Title = { {T}wistor holomorphic immersions of real surfaces into {K}\"ahler surfaces }, Journal = { Math.\ Ann. }, Volume = { 282 }, Pages = { 337-342 }, Year = { 1988 } } @Article{ Fin65, Author = { R. Finn }, Title = { {R}emarks relevant to minimal surfaces and surfaces of prescribed mean curvature }, Journal = { J. Analyse Math. }, Volume = { 14 }, Pages = { 139-160 }, Year = { 1965 } } @Incollection{ Fis92, Author = { A.E. Fischer }, Title = { {R}iemannian maps between {R}iemannian manifolds }, Booktitle = { {M}athematical aspects of classical field theory }, Editor = { M. Gotay and V.E. Moncrief and J.E. Marsden }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 132 }, Pages = { 331-366 }, Series = { Contemp.\ Math. }, Year = { 1992 } } @Article{ FisTro87, Author = { A. Fischer and A.J. Tromba }, Title = { {A} new proof that {T}eichm\"uller space is a cell. }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 303 }, Pages = { 257-262 }, Year = { 1987 } } @Article{ FisKoc87, Author = { W. Fischer and E. Koch }, Title = { {O}n 3-periodic minimal surfaces }, Journal = { Z. Krist. }, Volume = { 179 }, Pages = { 31-52 }, Year = { 1987 } } @Article{ FisKoc88, Author = { W. Fischer and E. Koch }, Title = { {O}n 3-periodic minimal surfaces with non-cubic symmetry }, Journal = { Z. Krist. }, Volume = { 183 }, Pages = { 129-152 }, Year = { 1988 } } @Article{ Fis80, Author = { D. Fischer-Colbrie }, Title = { {S}ome rigidity theorems for minimal submanifolds of the sphere }, Journal = { Acta Math. }, Volume = { 145 }, Pages = { 29-46 }, Year = { 1980 } } @Article{ Fis85, Author = { D. Fischer-Colbrie }, Title = { {O}n complete minimal surfaces with finite {M}orse index in three manifolds }, Journal = { Invent.\ Math. }, Volume = { 82 }, Pages = { 121-132 }, Year = { 1985 } } @Article{ FisSch80, Author = { D. Fischer-Colbrie and R. Schoen }, Title = { {T}he structure of complete stable minimal surfaces in {$3$}-manifolds of nonnegative scalar curvature }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 33 }, Pages = { 199-211 }, Year = { 1980 } } @Article{ Fla66, Author = { H. Flanders }, Title = { {R}emark on mean curvature }, Journal = { J. London Math.\ Soc. }, Volume = { 41 }, Pages = { 364-366 }, Year = { 1966 } } @Book{ FlaKli72, Author = { P. Flaschel and W. Klingenberg }, Title = { {R}iemannsche {H}ilbertmannigfaltigkeiten. {P}eriodische {G}eod\"atische }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 282 }, Series = { Lecture Notes in Math. }, Year = { 1972 } } @Book{ FolKoh72, Author = { G.B. Folland and J.J. Kohn }, Title = { {T}he {N}eumann problem for the {C}auchy--{R}iemann complex }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 75 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1972 } } @Article{ Fom70, Author = { A.T. Fomenko }, Title = { {R}ealization of cycles in compact symmetric spaces by totally geodesic submanifolds }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 195 }, Pages = { 789-792 }, Year = { 1970 } } @Article{ Fom70A, Author = { A.T. Fomenko }, Title = { {S}ome cases where elements of homotopy groups of homogeneous spaces are realized by totally geodesic spheres }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 11 }, Pages = { 792-795 }, Year = { 1970 } } @Article{ Fom71, Author = { A.T. Fomenko }, Title = { {B}ott periodicity from the point of view of an {$n$}-dimensional {D}irichlet functional }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 35 }, Pages = { 667-681 }, Year = { 1971 } } @Article{ Fom71A, Author = { A.T. Fomenko }, Title = { {T}he multi-dimensional {P}lateau problem in extraordinary theories of homology and cohomology }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 200 }, Pages = { 797-800 }, Year = { 1971 } } @Article{ Fom72, Author = { A.T. Fomenko }, Title = { {M}inimal compacta in {R}iemannian manifolds and {R}eifenberg's conjecture }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 36 }, Pages = { 1048-1079 }, Year = { 1972 } } @Article{ Fom72A, Author = { A.T. Fomenko }, Title = { {T}he multidimensional {P}lateau problem in {R}iemannian manifolds }, Journal = { Mat.\ Sb. }, Volume = { 89 }, Pages = { 475-519 }, Year = { 1972 } } @Article{ Fom72B, Author = { A.T. Fomenko }, Title = { {T}otally geodesic models of cycles }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 16 }, Pages = { 14-98 }, Note = { (Russian) }, Year = { 1972 } } @Article{ Fom73, Author = { A.T. Fomenko }, Title = { {G}eometric variational problems }, Journal = { Itogi Nauki Sovremennye Problemy Mat. }, Volume = { 1 }, Pages = { 39-60 }, Year = { 1973 } } @Article{ Fom74, Author = { A.T. Fomenko }, Title = { {M}ultidimensional {P}lateau problems on {R}iemannian manifolds, and extraordinary homology and cohomology theories, {I} }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 17 }, Pages = { 3-176 }, Note = { (Russian) }, Year = { 1974 } } @Book{ Fom74A, Author = { A.T. Fomenko }, Title = { {T}opologicheskie {V}ariatsionnye {Z}adachi ({T}opological {V}ariational {P}roblems) }, Publisher = { Moscow Univ.\ Press }, Address = { Moscow }, Note = { (Russian) }, Year = { 1974 } } @Article{ Fom78, Author = { A.T. Fomenko }, Title = { {M}ultidimensional {P}lateau problems on {R}iemannian manifolds, and extraordinary homology and cohomology theories, {I}{I} }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 18 }, Pages = { 4-93 }, Note = { (Russian) }, Year = { 1978 } } @Article{ Fom80, Author = { A.T. Fomenko }, Title = { {U}niversal lower bound on the growth rate of globally minimal solutions }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 251 }, Pages = { 295-299 }, Year = { 1980 } } @Article{ Fom81, Author = { A.T. Fomenko }, Title = { {M}ulti-dimensional variational methods in the topology of extremals }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 36 }, Pages = { 105-135 }, Year = { 1981 } } @Article{ Fom81A, Author = { A.T. Fomenko }, Title = { {O}n minimal volumes of topological globally minimal surfaces in cobordisms }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 45 }, Pages = { 187-212 }, Year = { 1981 } } @Book{ Fom82, Author = { A.T. Fomenko }, Title = { {V}ariatsionnie {M}etody v {T}opologii }, Publisher = { Nauka }, Address = { Moscow }, Year = { 1982 } } @Article{ Fom83, Author = { A.T. Fomenko }, Title = { {O}n the absolute minima of the volume functional and {D}irichlet functional on {R}iemannian manifolds }, Journal = { Vestnik Moskov.\ Univ.\ Ser.\ I Mat.\ Mekh. }, Volume = { 38 }, Pages = { 87-94 }, Year = { 1983 } } @Article{ Fom83A, Author = { A.T. Fomenko }, Title = { {T}he rate of growth and least volumes of globally minimal surfaces in cobordism }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 21 }, Pages = { 3-12 }, Note = { (Russian) }, Year = { 1983 } } @Incollection{ Fom84, Author = { A.T. Fomenko }, Title = { {O}n some properties of extremals of variational problems }, Booktitle = { {G}eometria i {T}opologia v {G}lobal'nykh {N}elineinykh {Z}adachakh ({G}eometry and {T}opology in {G}lobal {N}onlinear {P}roblems) }, Publisher = { Voronezh State University }, Address = { Voronezh }, Pages = { 114-122 }, Series = { Novoe Global Anal. }, Year = { 1984 } } @Book{ Fom90, Author = { A.T. Fomenko }, Title = { {T}he {P}lateau problem. {I} }, Publisher = { Gordon and Breach }, Address = { New York }, Year = { 1990 } } @Book{ Fom90A, Author = { A.T. Fomenko }, Title = { {T}he {P}lateau problem. {I}{I} }, Publisher = { Gordon and Breach }, Address = { New York }, Year = { 1990 } } @Incollection{ Fom93, Author = { A.T. Fomenko }, Title = { {M}inimization of length, area, and volume. {S}ome solved and some unsolved problems in the theory of minimal graphs and surfaces }, Booktitle = { {M}inimal surfaces }, Editor = { A.T. Fomenko }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 15 }, Pages = { 1-13 }, Series = { Adv.\ Soviet Math. }, Year = { 1993 } } @Article{ FomLeH88, Author = { A.T. Fomenko and Le~Hong~Van }, Title = { {L}agrangian manifolds and the {M}aslov index in the theory of minimal surfaces }, Journal = { Soviet Math.\ Dokl. }, Volume = { 37 }, Pages = { 330-333 }, Year = { 1988 } } @Article{ FomTuz86, Author = { A.T. Fomenko and A.A. Tuzhilin }, Title = { {M}ultivalued mappings, minimal surfaces and soap films }, Journal = { Vestnik Moskov.\ Univ.\ Ser.\ I Mat.\ Mekh. }, Pages = { 117-118 }, Year = { 1986 } } @Article{ ForHorZak84, Author = { P. Forgacz and Z. Horvath and W.J. Zakrzewski }, Title = { {C}lassical solutions of {${\bf {C}}{P}^{n-1}$} models in {$2+1$} dimensions }, Journal = { Nuclear Phys.\ B }, Volume = { 298 }, Pages = { 187-208 }, Year = { 1984 } } @Incollection{ For83, Author = { M. Forger }, Title = { {N}onlinear {$\sigma$}-models on symmetric spaces }, Booktitle = { {N}onlinear {P}artial {D}ifferential {O}perators and {Q}uantization procedures, {C}lausthal 1981 }, Editor = { S.I. Andersson and H.-D. Doebner }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1037 }, Series = { Lecture Notes in Math. }, Year = { 1983 } } @Article{ Fra94, Author = { S. Frankel }, Title = { {L}ocally symmetric and rigid factors for complex manifolds via harmonic maps }, Journal = { Ann.\ of Math. }, Volume = { 139 }, Pages = { 285-300 }, Year = { 1994 } } @Article{ Fra66, Author = { T. Frankel }, Title = { {O}n the fundamental group of a compact minimal submanifold }, Journal = { Ann.\ of Math. }, Volume = { 83 }, Pages = { 68-73 }, Year = { 1966 } } @Article{ Fra66A, Author = { T. Frankel }, Title = { {O}n theorems of {H}urwitz and {B}ochner }, Journal = { J. Math.\ Mech. }, Volume = { 15 }, Pages = { 373-378 }, Year = { 1966 } } @Incollection{ Fre85, Author = { D.S. Freed }, Title = { {F}lag manifolds and infinite dimensional {K}\"ahler geometry }, Booktitle = { {I}nfinite dimensional groups with applications }, Editor = { V. Kac }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 4 }, Pages = { 83-124 }, Series = { MSRI Publ. }, Year = { 1985 } } @Unpublished{ Fre85A, Author = { D.S. Freed }, Title = { {T}he geometry of loop groups }, Note = { M.I.T. Thesis }, Year = { 1985 } } @Article{ FreHasSco83, Author = { M. Freedman and J. Hass and P. Scott }, Title = { {L}east area incompressible surfaces in {$3$}-manifolds }, Journal = { Invent.\ Math. }, Volume = { 71 }, Pages = { 601-642 }, Year = { 1983 } } @Article{ Fre95, Author = { A. Freire }, Title = { {U}niqueness for the harmonic flow in two dimensions }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 3 }, Pages = { 95-105 }, Year = { 1995 } } @Article{ Fre95A, Author = { A. Freire }, Title = { {U}niqueness for the harmonic map flow from surfaces to general targets }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 70 }, Pages = { 310-338 }, Year = { 1995 } } @Article{ Fre96, Author = { A. Freire }, Title = { {C}orrection to : {U}niqueness for the harmonic map flow from surfaces to general targets }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 71 }, Pages = { 330-337 }, Year = { 1996 } } @Article{ FriTha83, Author = { H. Frid and F.J. Thayer }, Title = { {T}he {M}orse index theorem for elliptic problems with a constraint }, Journal = { An.\ Acad.\ Brasil.\ Ci\^enc. }, Volume = { 55 }, Pages = { 9-10 }, Year = { 1983 } } @Article{ FriTha90, Author = { H. Frid and F.J. Thayer }, Title = { {A}n abstract version of the {M}orse index theorem and its application to hypersurfaces of constant mean curvature }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 20 }, Pages = { 59-68 }, Year = { 1990 } } @Unpublished{ Fri, Author = { T. Friedrich }, Title = { {O}n superminimal surfaces }, Note = { preprint } } @Incollection{ Fri84, Author = { T. Friedrich }, Title = { {A}n application of the twistor theory to surfaces in {$4$}-dimensional manifolds }, Booktitle = { {P}roc. {C}onf. {D}ifferential {G}eometry and {A}pplications, {P}art 1, {N}ov{\'e} {M}{\v s}tona {M}orav{\v e} }, Publisher = { Charles University }, Address = { Prague }, Pages = { 43-45 }, Year = { 1984 } } @Article{ Fri84A, Author = { T. Friedrich }, Title = { {O}n surfaces in four-spaces }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 2 }, Pages = { 257-287 }, Year = { 1984 } } @Article{ Fri88, Author = { T. Friedrich }, Title = { {T}he geometry of {$t$}-holomorphic surfaces in {${S}^4$} }, Journal = { Math.\ Nachr. }, Volume = { 137 }, Pages = { 49-62 }, Year = { 1988 } } @Article{ FriGru85, Author = { T. Friedrich and R. Grunewald }, Title = { {O}n {E}instein metrics on the twistor space of a four-dimensional {R}iemannian manifold }, Journal = { Math.\ Nachr. }, Volume = { 123 }, Pages = { 55-60 }, Year = { 1985 } } @Unpublished{ FriLukZak92, Author = { Y. Frishman and J. Lukierski and W.J. Zakrzewski }, Title = { {Q}uantum group {$\sigma$} models }, Note = { Preprint }, Year = { 1992 } } @Article{ Fro86, Author = { C. Frohman }, Title = { {M}inimal surfaces and {H}eegaard slittings of the three-torus }, Journal = { Pacific J. Math. }, Volume = { 124 }, Pages = { 119-130 }, Year = { 1986 } } @Article{ Fro90, Author = { C. Frohman }, Title = { {T}he topological uniqueness of triply-periodic minimal surface in {${\bf {R}}^3$} }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 277-283 }, Year = { 1990 } } @Article{ FroHas89, Author = { C. Frohman and J. Hass }, Title = { {U}nstable minimal surfaces and {H}eegaard splittings }, Journal = { Invent.\ Math. }, Volume = { 95 }, Pages = { 529-540 }, Year = { 1989 } } @Misc{ FroMee, Author = { C. Frohman and W.H. Meeks }, Title = { {T}he topological uniqueness of complete one-ended minimal surfaces and {H}eegaard surfaces in {${\bf {R}}^3$} } } @Article{ Fu96, Author = { J.X. Fu }, Title = { {H}armonicity of {R}iemannian maps and {G}aussian maps }, Journal = { J. Hangzhou Univ. }, Volume = { 23 }, Pages = { 15--22 }, Note = { (Chinese) }, Year = { 1996 } } @Unpublished{ Fuc, Author = { M. Fuchs }, Title = { {$p$}-harmonic obstacle problems. {P}art {I}{V}: {U}nbounded side conditions }, Note = { preprint } } @Misc{ FucA, Author = { M. Fuchs }, Title = { {H}\"older continuity of the gradient for degenerate variational inequalities {N}onlinear {A}nalysis } } @Misc{ FucB, Author = { M. Fuchs }, Title = { {R}egularit\"atstheorie f\"ur {M}inimalstellen von degenerierten {V}ariationsintegralen mit nichtlinearen {N}ebenbedingen: {$p$}-harmonische {H}indernisprobleme } } @Article{ Fuc85, Author = { M. Fuchs }, Title = { {S}ome remarks on the boundary regularity for minima of variational problems with obstacles }, Journal = { Manuscripta Math. }, Volume = { 54 }, Pages = { 107-119 }, Year = { 1985 } } @Article{ Fuc85A, Author = { M. Fuchs }, Title = { {V}ariational inequalities for vector valued functions with non-convex obstacles }, Journal = { Analysis }, Volume = { 5 }, Pages = { 223-238 }, Year = { 1985 } } @Article{ Fuc86, Author = { M. Fuchs }, Title = { {E}in {R}egularit\"atssatz for ein lineares {S}ystem von {V}ariationsungleichen mit einer {H}albraumnebenbedingung }, Journal = { Z. Anal.\ Anwendungen }, Volume = { 5 }, Pages = { 47-57 }, Year = { 1986 } } @Article{ Fuc87, Author = { M. Fuchs }, Title = { {A}n elementary partial regularity proof for vector valued obstacle problems }, Journal = { Math.\ Ann. }, Year = { 1987 } } @Article{ Fuc87A, Author = { M. Fuchs }, Title = { {E}verywhere regularity theorem for mappings which minimize {$p$}-energy }, Journal = { Comment.\ Math.\ Univ.\ Carolin. }, Volume = { 28 }, Pages = { 673-677 }, Year = { 1987 } } @Article{ Fuc87B, Author = { M. Fuchs }, Title = { {L}iouville theorem for {$p$}-harmonic systems }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 1 }, Pages = { 429-435 }, Year = { 1987 } } @Article{ Fuc87C, Author = { M. Fuchs }, Title = { {A} {L}iouville theorem for mappings which minimize {$p$}-energy }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 7 }, Pages = { 429-435 }, Year = { 1987 } } @Article{ Fuc87D, Author = { M. Fuchs }, Title = { {A} note on removable singularities for minima of certain vector-valued obstacle problems }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 48 }, Pages = { 521-525 }, Year = { 1987 } } @Article{ Fuc87E, Author = { M. Fuchs }, Title = { {A} regularity theorem for energy minimizing maps of {R}iemannian manifolds }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 12 }, Pages = { 1309-1321 }, Year = { 1987 } } @Article{ Fuc89, Author = { M. Fuchs }, Title = { {$p$}-harmonic obstacle problems, {P}art {I}{I} }, Journal = { Manuscripta Math. }, Volume = { 63 }, Pages = { 381-419 }, Year = { 1989 } } @Article{ Fuc89A, Author = { M. Fuchs }, Title = { {S}ome regularity theorems for mappings which are stationary points for the {$p$}-energy functional }, Journal = { Analysis }, Volume = { 9 }, Pages = { 127-143 }, Year = { 1989 } } @Article{ Fuc90, Author = { M. Fuchs }, Title = { {$p$}-harmonic obstacle problems, {P}art {I} }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 156 }, Pages = { 127-158 }, Year = { 1990 } } @Article{ Fuc90A, Author = { M. Fuchs }, Title = { {$p$}-harmonic obstacle problems, {P}art {I}{I}{I} }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 156 }, Pages = { 159-180 }, Year = { 1990 } } @Article{ Fuc91, Author = { M. Fuchs }, Title = { {H}ypersurfaces of prescribed mean curvature enclosing a given body }, Journal = { Manuscripta Math. }, Volume = { 72 }, Pages = { 131-140 }, Year = { 1991 } } @Article{ Fuc92, Author = { M. Fuchs }, Title = { {S}moothness for system of degenerate variational inequalities with natural growth }, Journal = { Comment.\ Math.\ Univ.\ Carolin. }, Volume = { 33 }, Pages = { 33-41 }, Year = { 1992 } } @Article{ Fuc93, Author = { M. Fuchs }, Title = { {T}he blow-up of {$p$}-harmonic maps }, Journal = { Manuscripta Math. }, Volume = { 81 }, Pages = { 89-94 }, Year = { 1993 } } @Article{ FucFus88, Author = { M. Fuchs and N. Fusco }, Title = { {P}artial regularity results for vector valued functions which minimize certain functionals having non quadratic growth under smooth side conditions }, Journal = { J. Reine Angew.\ Math. }, Volume = { 390 }, Pages = { 67-78 }, Year = { 1988 } } @Misc{ FucSer, Author = { M. Fuchs and G. Seregin }, Title = { {H}\"older continuity for weak extremals of some two-dimensional variational problems related to nonlinear elasticity } } @Article{ Fug78, Author = { B. Fuglede }, Title = { {H}armonic morphisms between {R}iemannian manifolds }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 28 }, Pages = { 107-144 }, Year = { 1978 } } @Incollection{ Fug79, Author = { B. Fuglede }, Title = { {H}armonic morphisms }, Booktitle = { {C}omplex {A}nalysis {J}oensuu 1978 }, Editor = { I. Laine and O. Lehto and T. Sorvali }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 747 }, Pages = { 123-135 }, Series = { Lecture Notes in Math. }, Year = { 1979 } } @Article{ Fug82, Author = { B. Fuglede }, Title = { {A} criterion of non-vanishing differential of a smooth map }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 14 }, Pages = { 98-102 }, Year = { 1982 } } @Article{ Fug87, Author = { B. Fuglede }, Title = { {F}inely holomorphic functions and finely harmonic morphisms }, Journal = { Aequationes Math. }, Volume = { 34 }, Pages = { 167-173 }, Year = { 1987 } } @Article{ Fug96, Author = { B. Fuglede }, Title = { {H}armonic morphisms between semi-{R}iemannian manifolds }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { 21 }, Pages = { 31-50 }, Year = { 1996 } } @Article{ Fuj85, Author = { K. Fujii }, Title = { {A} classical solution of the non-linear complex {G}rassmann {$\sigma$}-model with higher derivatives }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 101 }, Pages = { 207-211 }, Year = { 1985 } } @Article{ Fuj85A, Author = { K. Fujii }, Title = { {C}lassical solutions of higher dimensional non-linear sigma models on spheres }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 10 }, Pages = { 49-54 }, Year = { 1985 } } @Unpublished{ Fuj92, Author = { K. Fujii }, Title = { {A} relation between instantons of {G}rassmannian {$\sigma$}-models and {T}oda equations: {C}omments to the paper of {D}{J}{P}{T} }, Note = { Yokohama preprint }, Year = { 1992 } } @Unpublished{ Fuj92A, Author = { K. Fujii }, Title = { {A} relation between instantons of {G}rassmannian {$\sigma$}-models and {T}oda equations {I}{I}{I} }, Note = { Yokohama preprint }, Year = { 1992 } } @Article{ Fuj92B, Author = { K. Fujii }, Title = { {A} relation between instantons of {G}rassmannian {$\sigma$}-models and {T}oda equations {I}{I} }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 25 }, Pages = { 203-211 }, Year = { 1992 } } @Article{ Fuj93, Author = { K. Fujii }, Title = { {N}onlinear {G}rassmann {$\sigma$}-models, {T}oda equations and self-dual {E}instein equations: {S}upplements to the preceding papers }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 27 }, Pages = { 117-122 }, Year = { 1993 } } @Unpublished{ Fuj94, Author = { K. Fujii }, Title = { {C}{P}-invariance and nonlinear sigma models: geometry and physics }, Note = { Preprint }, Year = { 1994 } } @Unpublished{ Fuj94A, Author = { K. Fujii }, Title = { {S}olutions of {${A}_{\infty}$} {T}oda equations based on non-compact group {${S}{U}(1,1)$} and infinite dimensional {G}rassmann manifolds }, Note = { Preprint }, Year = { 1994 } } @Article{ FujKoiSas84, Author = { K. Fujii and T. Koikawa and R. Sasaki }, Title = { {C}lassical solutions for the supersymmetric {G}rassmannian sigma models in two dimensions {I} }, Journal = { Progr.\ Theoret.\ Phys. }, Volume = { 71 }, Pages = { 388-394 }, Year = { 1984 } } @Article{ FujSas84, Author = { K. Fujii and R. Sasaki }, Title = { {C}lassical solutions for the supersymmetric {G}rassmannian sigma models in two dimensions {I}{I} }, Journal = { Progr.\ Theoret.\ Phys. }, Volume = { 71 }, Pages = { 831-839 }, Year = { 1984 } } @Article{ Fuj86, Author = { M. Fujiki }, Title = { {O}n the {G}auss map of minimal surfaces immersed in {${R}^n$} }, Journal = { Kodai Math.\ J. }, Volume = { 9 }, Pages = { 44-49 }, Year = { 1986 } } @Misc{ Fuj, Author = { H. Fujimoto }, Title = { {M}odified defect relations for the {G}auss map of minimal surfaces } } @Article{ Fuj83, Author = { H. Fujimoto }, Title = { {O}n the {G}auss map of a complete minimal surface in {${\bf {R}}^m$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 35 }, Pages = { 279-288 }, Year = { 1983 } } @Article{ Fuj83A, Author = { H. Fujimoto }, Title = { {V}alue distribution of the {G}auss maps of complete minimal surfaces in {${\bf {R}}^m$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 35 }, Pages = { 663-681 }, Year = { 1983 } } @Article{ Fuj88, Author = { H. Fujimoto }, Title = { {O}n the number of exceptional values of the {G}auss map of minimal surfaces }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 40 }, Pages = { 235-247 }, Year = { 1988 } } @Article{ Fuj91, Author = { H. Fujimoto }, Title = { {U}nicity theorems for the {G}auss maps of complete minimal surfaces {I}{I} }, Journal = { Kodai Math.\ J. }, Volume = { 16 }, Pages = { 335-354 }, Year = { 1991 } } @Article{ Fuj93A, Author = { H. Fujimoto }, Title = { {S}ome function-theoretic properties of the {G}auss map of minimal surfaces }, Journal = { S{\^u}rikaisekikenky{\^u}sho K{\^o}ky{\^u}roku }, Volume = { 819 }, Pages = { 35-49 }, Year = { 1993 } } @Article{ FujA, Author = { A. Fujioka }, Title = { {M}inimizing tangent maps from 3-ball to complex projective spaces }, Journal = { J. Fac.\ Sci.\ Univ.\ Tokyo Sect.\ IA Math. }, Volume = { 40 }, Pages = { 125-139 } } @Unpublished{ Fuj94B, Author = { A. Fujioka }, Title = { {H}armonic maps and associated maps from a {R}iemann surface into the {$3$}-dimensional space forms }, Note = { Preprint }, Year = { 1994 } } @Article{ Fuj95, Author = { A. Fujioka }, Title = { {H}armonic maps and associated maps from simply connected {R}iemann surfaces into the {$3$}-dimensional space forms }, Journal = { T\^ohoku Math.\ J. }, Volume = { 47 }, Pages = { 431-439 }, Year = { 1995 } } @Article{ Ful54, Author = { F.B. Fuller }, Title = { {H}armonic mappings }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 40 }, Pages = { 987-991 }, Year = { 1954 } } @Article{ Fur94, Author = { H. Furuhata }, Title = { {C}onstruction and classification of isometric minimal immersions of {K}\"ahler manifolds into {E}uclidean spaces }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 26 }, Pages = { 487-496 }, Year = { 1994 } } @Article{ FurGueKot94, Author = { M. Furuta and M.A. Guest and M. Kotani and Y. Ohnita }, Title = { {O}n the fundamental group of the space of harmonic {$2$}-spheres in the {$n$}-sphere }, Journal = { Math.\ Z. }, Volume = { 215 }, Pages = { 503-518 }, Year = { 1994 } } @Article{ Fut80, Author = { A. Futaki }, Title = { {N}on-existence of minimizing harmonic maps from {$2$}-spheres }, Journal = { Proc.\ Japan Acad.\ Ser.\ A Math.\ Sci. }, Volume = { 56 }, Pages = { 291-293 }, Year = { 1980 } } @Article{ Fut80A, Author = { A. Futaki }, Title = { {O}n the uniqueness of the {D}irichlet problem for harmonic maps }, Journal = { J. Fac.\ Sci.\ Univ.\ Tokyo Sect.\ IA Math. }, Volume = { 27 }, Pages = { 181-192 }, Year = { 1980 } } @Unpublished{ Gac80, Author = { F. Gackstatter }, Title = { {L}ectures on minimal surfaces }, Note = { Dept. Mat. U.S.P. S\~ao Paolo }, Year = { 1980 } } @Article{ GacKun77, Author = { F. Gackstatter and R. Kunert }, Title = { {K}onstruktion vollst{\"a}ndiger {M}inimalfl{\"a}chen von endlicher {G}esamtkr{\"u}mmung }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 65 }, Pages = { 289-297 }, Year = { 1977 } } @Article{ Gag83, Author = { M. Gage }, Title = { {A}n isoparametric inequality with applications to curve shortening }, Journal = { Duke Math.\ J. }, Volume = { 50 }, Pages = { 1225-1229 }, Year = { 1983 } } @Article{ Gag84, Author = { M. Gage }, Title = { {C}urve shortening makes convex curves circular }, Journal = { Invent.\ Math. }, Volume = { 76 }, Pages = { 357-364 }, Year = { 1984 } } @Article{ GagHam86, Author = { M. Gage and R.S. Hamilton }, Title = { {T}he heat equation shrinking convex plane curves }, Journal = { J. Differential Geom. }, Volume = { 23 }, Pages = { 69-96 }, Year = { 1986 } } @Article{ Gal81, Author = { G.J. Galloway }, Title = { {S}ome results on the occurence of compact minimal submanifolds }, Journal = { Manuscripta Math. }, Volume = { 35 }, Pages = { 209-219 }, Year = { 1981 } } @Article{ Gal84, Author = { G.J. Galloway }, Title = { {C}losed timelike geodesics }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 285 }, Pages = { 379-388 }, Year = { 1984 } } @Article{ GalRod91, Author = { G.J. Galloway and L. Rodriguez }, Title = { {I}ntersections of minimal submanifolds }, Journal = { Geom.\ Dedicata }, Volume = { 39 }, Pages = { 29-42 }, Year = { 1991 } } @Article{ Gao93, Author = { J.M. Gao }, Title = { {S}ome results on hyperbolic harmonic maps }, Journal = { C. R. Math.\ Rep.\ Acad.\ Sci.\ Canada }, Volume = { 15 }, Pages = { 19-24 }, Year = { 1993 } } @Misc{ GarVanVaz, Author = { E. Garc{\'i}a-R{\'i}o and L. Vanhecke and M.E. Vazquez-Abal }, Title = { {H}armonic connections } } @Article{ GarVanVazA, Author = { E. Garc{\'i}a-R{\'i}o and L. Vanhecke and M.E. Vazquez-Abal }, Title = { {H}armonic endomorphism fields }, Journal = { Illinois J. Math. }, Note = { (to appear) } } @Article{ GarVanVazB, Author = { E. Garc{\'i}a-R{\'i}o and L. Vanhecke and M.E. Vazquez-Abal }, Title = { {T}angent bundles of order {$r$} and harmonicity of induced maps }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Note = { (to appear) } } @Article{ Gas92, Author = { A. Gastel }, Title = { {R}egularity of minimizing harmonic mappings into ellipsoids and similar other manifolds }, Journal = { Manuscripta Math. }, Volume = { 77 }, Pages = { 97-104 }, Year = { 1992 } } @Article{ Gau89, Author = { H. Gauchman }, Title = { {P}inching theorems for totally real minimal submanifolds of {${\bf {C}} {P}(c)$} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 41 }, Pages = { 249-257 }, Year = { 1989 } } @Article{ GauGla94, Author = { H. Gauchman and J.F. Glazebrook }, Title = { {H}olomorphic maps of {K}{\"a}hler manifolds with constrained energy density }, Journal = { Geom.\ Dedicata }, Volume = { 52 }, Pages = { 221-226 }, Year = { 1994 } } @Misc{ GauTot, Author = { H. Gauchman and G. Toth }, Title = { {F}ine structure of the space of spherical minimal immersions } } @Article{ GauTot94, Author = { H. Gauchman and G. Toth }, Title = { {C}onstructions of harmonic polynomial maps between spheres }, Journal = { Geom.\ Dedicata }, Volume = { 50 }, Pages = { 57-79 }, Year = { 1994 } } @Article{ GauTot94A, Author = { H. Gauchman and G. Toth }, Title = { {R}eal orthogonal multiplications in codimension two }, Journal = { Nova J. of Algebra and Geometry }, Volume = { 3 }, Note = { (to appear) }, Year = { 1994 } } @Misc{ Gau, Author = { P. Gauduchon }, Title = { {L}es structures holomorphes du fibr{\'e} tangent vertical sur l'espace des twisteurs d'und vari{\'e}t{\'e} conforme auto-duale {\`a} premier nombre de {B}etti non-nul } } @Incollection{ GauA, Author = { P. Gauduchon }, Title = { {T}wisteurs et applications harmoniques en dimension {$4$} }, Booktitle = { {S}{\'e}minaire de th{\'e}orie spectrale et g{\'e}om{\'e}trie, {C}hamb{\'e}ry-{G}renoble 1985-86 }, Pages = { 35-93 } } @Article{ Gau86, Author = { P. Gauduchon }, Title = { {P}seudo-immersions superminimales d'une surface de {R}iemann dans une vari\'et\'e riemannienne de dimension {$4$} }, Journal = { Bull.\ Soc.\ Math.\ France }, Volume = { 114 }, Pages = { 447-508 }, Year = { 1986 } } @Incollection{ Gau87, Author = { P. Gauduchon }, Title = { {L}a correspondance de {B}ryant }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 181-208 }, Series = { Ast\'erisque }, Year = { 1987 } } @Incollection{ Gau87A, Author = { P. Gauduchon }, Title = { {L}es immersions super-minimales d'une surface compacte dans une vari\'et\'e orient\'ee de dimension {$4$} }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 151-180 }, Series = { Ast\'erisque }, Year = { 1987 } } @Article{ GauLaw85, Author = { P. Gauduchon and H.B. Lawson }, Title = { {T}opologically nonsingular minimal cones }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 34 }, Pages = { 915-927 }, Year = { 1985 } } @Article{ GavMaz87, Author = { B. Gaveau and E. Mazet }, Title = { {M}\'ethode de plus grande descente pour la construction du probl\`eme de {P}lateau }, Journal = { Bull.\ Soc.\ Math.\ France }, Volume = { 111 }, Pages = { 111-187 }, Year = { 1987 } } @Article{ GehHaa60, Author = { F.W. Gehring and H. Haati }, Title = { {T}he transformations which preserve the harmonic functions }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { A293 }, Pages = { 3-12 }, Year = { 1960 } } @Article{ Ger80, Author = { C. Gerhardt }, Title = { {E}volutionary surfaces of prescribed mean curvature }, Journal = { J. Differential Equations }, Volume = { 36 }, Pages = { 139-172 }, Year = { 1980 } } @Article{ Ger90, Author = { C. Gerhardt }, Title = { {F}low of nonconvex hypersurfaces into spheres }, Journal = { J. Differential Geom. }, Volume = { 32 }, Pages = { 299-314 }, Year = { 1990 } } @Article{ GerRau54, Author = { M. Gerstenhaber and H.E. Rauch }, Title = { {O}n extremal quasi-conformal mappings, {I} }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 40 }, Pages = { 808-812 }, Year = { 1954 } } @Article{ GerRau54A, Author = { M. Gerstenhaber and H.E. Rauch }, Title = { {O}n extremal quasi-conformal mappings, {I}{I} }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 40 }, Pages = { 991-994 }, Year = { 1954 } } @Article{ GhiVis80, Author = { G. Ghika and M. Visinescu }, Title = { {C}onstraints of a generally covariant four dimensional sigma model }, Journal = { Phys.\ Lett.\ B }, Volume = { 93 }, Pages = { 411-415 }, Year = { 1980 } } @Article{ GhiVis80A, Author = { G. Ghika and M. Visinescu }, Title = { {F}our dimensional sigma model coupled to the metric tensor field }, Journal = { Nuovo Cimento B }, Volume = { 59 }, Pages = { 59-74 }, Year = { 1980 } } @Article{ GhiVis80B, Author = { G. Ghika and M. Visinescu }, Title = { {G}ribov vacuum copies in terms of harmonic maps }, Journal = { Phys.\ Rev.\ D }, Volume = { 21 }, Pages = { 1538-1542 }, Year = { 1980 } } @Article{ GhiVis80C, Author = { G. Ghika and M. Visinescu }, Title = { {V}acuum degeneracies in terms of harmonic maps }, Journal = { Phys.\ Rev.\ D }, Year = { 1980 } } @Article{ GhiVis82, Author = { G. Ghika and M. Visinescu }, Title = { {M}eron solution of the sigma model and singular harmonic maps }, Journal = { Z. Phys. }, Volume = { C11 }, Pages = { 353-357 }, Year = { 1982 } } @Incollection{ Gia82, Author = { M. Giaquinta }, Title = { {T}he regularity problem of extremals of variational integrals }, Booktitle = { {S}ystems of nonlinear {P}.{D}.{E}. }, Publisher = { Oxford University Press }, Year = { 1982 } } @Book{ Gia83, Author = { M. Giaquinta }, Title = { {M}ultiple integrals in the calculus of variations and nonlinear elliptic systems }, Publisher = { Princeton Univ.\ Press. }, Address = { Princeton }, Volume = { 105 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Incollection{ Gia86, Author = { M. Giaquinta }, Title = { {T}he problem of the regularity of minimizers }, Booktitle = { {I}{C}{M} {B}erkeley }, Year = { 1986 } } @Article{ Gia87, Author = { M. Giaquinta }, Title = { {G}rowth conditions and regularity, a counterexample }, Journal = { Manuscripta Math. }, Volume = { 59 }, Pages = { 245-248 }, Year = { 1987 } } @Unpublished{ Gia87A, Author = { M. Giaquinta }, Title = { {Q}uasiconvexity, growth conditions and partial regularity }, Note = { Bonn preprint }, Year = { 1987 } } @Article{ Giacek85, Author = { M. Giaquinta and J. Sou{\v c}ek }, Title = { {H}armonic maps into a hemisphere }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 12 }, Pages = { 81-90 }, Year = { 1985 } } @Article{ GiaGiu78, Author = { M. Giaquinta and E. Giusti }, Title = { {N}onlinear elliptic systems with quadratic growth }, Journal = { Manuscripta Math. }, Volume = { 24 }, Pages = { 323-349 }, Year = { 1978 } } @Unpublished{ GiaGiu82, Author = { M. Giaquinta and E. Giusti }, Title = { {D}ifferentiablity of minima of non differentiable functionals }, Note = { University of Firenze }, Year = { 1982 } } @Article{ GiaGiu82A, Author = { M. Giaquinta and E. Giusti }, Title = { {O}n the regularity of the minima of variational integrals }, Journal = { Acta Math. }, Volume = { 148 }, Pages = { 31-46 }, Year = { 1982 } } @Unpublished{ GiaGiu83, Author = { M. Giaquinta and E. Giusti }, Title = { {S}harp estimates for the derivatives of local minima of variational integrals }, Note = { University of Firenze }, Year = { 1983 } } @Unpublished{ GiaGiu84, Author = { M. Giaquinta and E. Giusti }, Title = { {R}esearches on the statics of masonry structures }, Note = { Univ. Firenze, preprint }, Year = { 1983/84 } } @Article{ GiaGiu84A, Author = { M. Giaquinta and E. Giusti }, Title = { {Q}uasi minima }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 1 }, Pages = { 79-107 }, Year = { 1984 } } @Article{ GiaGiu84B, Author = { M. Giaquinta and E. Giusti }, Title = { {T}he singular set of the minima of certain quadratic functionals }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 9 }, Pages = { 45-55 }, Year = { 1984 } } @Unpublished{ GiaHil81, Author = { M. Giaquinta and S. Hildebrandt }, Title = { {E}stimations a priori des solutions faibles de certains syst\`emes non lin\'eaires elliptiques }, Number = { 17 }, Note = { S\'eminaire Goulaouic--Meyer--Schwartz }, Year = { 1980-81 } } @Article{ GiaHil82, Author = { M. Giaquinta and S. Hildebrandt }, Title = { {A} priori estimates of harmonic mappings }, Journal = { J. Reine Angew.\ Math. }, Volume = { 336 }, Pages = { 124-164 }, Year = { 1982 } } @Article{ GiaMod79, Author = { M. Giaquinta and G. Modica }, Title = { {R}egularity results for some classes of higher order non linear elliptic systems }, Journal = { J. Reine Angew.\ Math. }, Volume = { 311/312 }, Pages = { 145-169 }, Year = { 1979 } } @Article{ GiaMod86, Author = { M. Giaquinta and G. Modica }, Title = { {P}artial regularity of minimizers of quasiconvex integrals }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 3 }, Pages = { 185-208 }, Year = { 1986 } } @Article{ GiaMod87, Author = { M. Giaquinta and G. Modica }, Title = { {R}emarks on the regularity of the minimizers of certain degenerate functionals }, Journal = { Manuscripta Math. }, Volume = { 57 }, Pages = { 55-99 }, Year = { 1987 } } @Misc{ GiaModcek, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {V}ariational problems for the conformally invariant integral {$\int \vert du\vert^n$} } } @Article{ GiaModcek79, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {F}unctionals with linear growth in the calculus of variations {I} }, Journal = { Comment.\ Math.\ Univ.\ Carolin. }, Volume = { 20 }, Pages = { 143-172 }, Year = { 1979 } } @Article{ GiaModcek89, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {C}artesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 106 }, Pages = { 97-159 }, Year = { 1989 } } @Article{ GiaModcek89A, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {C}artesian currents and variational problems for mappings into spheres }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 16 }, Pages = { 393-485 }, Year = { 1989 } } @Article{ GiaModcek89B, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {T}he {D}irichlet energy of mappings with values into the sphere }, Journal = { Manuscripta Math. }, Volume = { 65 }, Pages = { 489-507 }, Year = { 1989 } } @Article{ GiaModcek90, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {E}rratum/{A}ddendum }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 109 }, Pages = { 385-392 }, Note = { (See 106 (1989) 97-159) }, Year = { 1990 } } @Article{ GiaModcek90A, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {L}iquid crystals: {R}elaxed energies, dipoles, singular lines and singular points }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 17 }, Pages = { 415-437 }, Year = { 1990 } } @Incollection{ GiaModcek91, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {C}artesian currents and liquid crystals, dipoles, singular lines and singular points }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 113-127 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Unpublished{ GiaModcek91A, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {T}he gap phenomenon for variational integrals in {S}obolev spaces }, Note = { Preprint, Univ. Firenze }, Year = { 1991 } } @Article{ GiaModcek92, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {T}he {D}irichlet integral for mappings between manifolds: {C}artesian currents and homology }, Journal = { Math.\ Ann. }, Volume = { 294 }, Pages = { 325-386 }, Year = { 1992 } } @Article{ GiaModcek93, Author = { M. Giaquinta and G. Modica and J. Sou{\v c}ek }, Title = { {V}ariational problems for maps of bounded variation with values in {${S}^1$} }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 87-121 }, Year = { 1993 } } @Article{ GiaStr81, Author = { M. Giaquinta and M. Struwe }, Title = { {A}n optimal regularity result for a class of quasilinear parabolic systems }, Journal = { Manuscripta Math. }, Volume = { 36 }, Pages = { 223-239 }, Year = { 1981 } } @Book{ Gig83, Author = { G. Gigante }, Title = { {A} note on harmonic morphisms }, Publisher = { Preprint Univ.\ Camerino }, Year = { 1983 } } @Article{ Gig83A, Author = { G. Gigante }, Title = { {R}emarks on subharmonic functions on {R}iemannian manifolds }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 133 }, Pages = { 257-266 }, Year = { 1983 } } @Article{ Gil73, Author = { P. Gilkey }, Title = { {C}urvature and the eigenvalues of the {L}aplacian for elliptic complexes }, Journal = { Adv.\ in Math. }, Volume = { 10 }, Pages = { 344-382 }, Year = { 1973 } } @Article{ Gil78, Author = { P. Gilkey }, Title = { {S}mooth invariants of a {R}iemannian manifold }, Journal = { Adv.\ in Math. }, Volume = { 28 }, Pages = { 1-10 }, Year = { 1978 } } @Article{ Gil50, Author = { P. Gillis }, Title = { {E}quations de {M}onge--{A}mp\`ere \`a quatre variables ind\'ependantes }, Journal = { Bull.\ Cl.\ Sc.\ Acad.\ Roy.\ Belg. }, Volume = { 36 }, Pages = { 474-484 }, Year = { 1950 } } @Article{ Gil51, Author = { P. Gillis }, Title = { {E}quations de {M}onge--{A}mp\`ere \`a six variables ind\'ependantes }, Journal = { Bull.\ Cl.\ Sc.\ Acad.\ Roy.\ Belg. }, Volume = { 37 }, Pages = { 229-240 }, Year = { 1951 } } @Article{ Gil51A, Author = { P. Gillis }, Title = { {S}ur certaines \'equations de {M}onge--{A}mp\`ere du calcul des variations }, Journal = { Bull.\ Soc.\ Math.\ Belg. }, Pages = { 38-50 }, Year = { 1951 } } @Article{ GinVel82, Author = { J. Ginibre and G. Velo }, Title = { {T}he {C}auchy problem for the {$0({N}), {\bf {C}}{P}(n-1)$} and {${G}{\bf {C}}({N},p)$}-models }, Journal = { Ann.\ Physics }, Volume = { 142 }, Pages = { 393-415 }, Year = { 1982 } } @Book{ Giu84, Author = { E. Giusti }, Title = { {M}inimal surfaces and functions of bounded variation }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 80 }, Series = { Monographs Math. }, Year = { 1984 } } @Unpublished{ GlaSto79, Author = { V. Glaser and R. Stora }, Title = { {R}egular solutions of the {${\bf {C}}{P}^n$} models and further generalizations }, Note = { CERN preprint }, Year = { 1979 } } @Article{ GlaSarSch65, Author = { M. Glasner and L. Sario and M. Schiffer }, Title = { {T}he span and principal functions in {R}iemannian spaces }, Journal = { J. Analyse Math. }, Volume = { 15 }, Pages = { 115-134 }, Year = { 1965 } } @Unpublished{ Gla83, Author = { J.F. Glazebrook }, Title = { {I}sotropic harmonic maps to complex hyperbolic space forms }, Note = { Univ. Warwick preprint }, Year = { 1983 } } @Article{ Gla84, Author = { J.F. Glazebrook }, Title = { {T}he construction of a class of harmonic maps to quaternionic projective space }, Journal = { J. London Math.\ Soc. }, Volume = { 30 }, Pages = { 151-159 }, Year = { 1984 } } @Article{ Gla84A, Author = { J.F. Glazebrook }, Title = { {H}armonic maps of {R}ieman surfaces to indefinite complex {G}rassmannians and the classical domains }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 48 }, Pages = { 108-120 }, Year = { 1984 } } @Unpublished{ Gla84B, Author = { J.F. Glazebrook }, Title = { {I}sotropic harmonic maps to {K}\"ahler manifolds and related properties }, Note = { Warwick Ph.D Thesis }, Year = { 1984 } } @Incollection{ Gla86, Author = { J.F. Glazebrook }, Title = { {O}n isotropic harmonic maps to real and quaternionic {G}rassmannians }, Booktitle = { {C}omplex differential geometry and non-linear differential equations }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 49 }, Pages = { 51-61 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Incollection{ Gla87, Author = { J.F. Glazebrook }, Title = { {H}armonic maps of {R}iemann surfaces to quaternionic projective spaces and {G}rassmannians }, Booktitle = { {T}he {L}efschetz centennial conference, {P}art {I}{I}{I}: proceedings on differential equations }, Editor = { A. Verjovsky }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 58.3 }, Pages = { 107-121 }, Series = { Contemp.\ Math. }, Year = { 1987 } } @Article{ Gla89, Author = { J.F. Glazebrook }, Title = { {A}n inequality for harmonic maps of compact {K}\"ahler manifolds that implies holomorphicity }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 107 }, Pages = { 261-269 }, Year = { 1989 } } @Article{ Gla89A, Author = { J.F. Glazebrook }, Title = { {P}luriharmonic maps of compact {K}\"ahler manifolds to quaternionic projective space }, Journal = { Tensor (N.S.) }, Volume = { 48 }, Pages = { 143-148 }, Year = { 1989 } } @Article{ Gla90, Author = { J.F. Glazebrook }, Title = { {S}trings, harmonic maps and hyperbolic systems }, Journal = { Comput.\ Math.\ Appl. }, Volume = { 19 }, Pages = { 117-125 }, Year = { 1990 } } @Article{ GlaRon92, Author = { J.F. Glazebrook and G. Ronsse }, Title = { {O}n pluriharmonic maps to quaternionic projective spaces and totally complex immersions }, Journal = { Tensor (N.S.) }, Volume = { 51 }, Pages = { 48-52 }, Year = { 1992 } } @Article{ GleWol91, Author = { S. Gleason and T.H. Wolff }, Title = { {L}ewy's harmonic gradient maps in higher dimensions }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 16 }, Pages = { 1925-1968 }, Year = { 1991 } } @Article{ Glu88, Author = { H. Gluck }, Title = { {G}eodesics in the unit tangent bundle of a round sphere }, Journal = { Enseign.\ Math. }, Volume = { 34 }, Pages = { 233-246 }, Year = { 1988 } } @Article{ GluMorZil89, Author = { H. Gluck and F. Morgan and W. Ziller }, Title = { {C}alibrated geometries in {G}rassmann manifolds }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 64 }, Pages = { 256-268 }, Year = { 1989 } } @Article{ GluWarYan83, Author = { H. Gluck and F. Warner and C.T. Yang }, Title = { {D}ivision algebras, fibrations of spheres by great spheres and the topolgoical determination of space by the gross behavior of its geodesics }, Journal = { Duke Math.\ J. }, Volume = { 50 }, Pages = { 1041-1076 }, Year = { 1983 } } @Misc{ GluWarZil, Author = { H. Gluck and F. Warner and W. Ziller }, Title = { {F}ibrations of spheres by parallel great spheres } } @Article{ GluZil86, Author = { H. Gluck and W. Ziller }, Title = { {O}n the volume of a unit vector field on the three-sphere }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 41 }, Pages = { 177-192 }, Year = { 1986 } } @Incollection{ Gol73, Author = { S.I. Goldberg }, Title = { {L}iouville's theorem for a class of quasiconformal mappings }, Booktitle = { {G}reek {M}ath. {S}oc. {C}. {C}aratheodory {S}ymp. }, Pages = { 154-164 }, Year = { 1973 } } @Article{ Gol75, Author = { S.I. Goldberg }, Title = { {O}n the distance decreasing property of a class of real harmonic mappings }, Journal = { Geom.\ Dedicata }, Volume = { 14 }, Pages = { 61-69 }, Year = { 1975 } } @Article{ Gol76, Author = { S.I. Goldberg }, Title = { {M}appings of nonpositively curved manifolds }, Journal = { Nagoya Math.\ J. }, Volume = { 61 }, Pages = { 73-84 }, Year = { 1976 } } @Incollection{ Gol92, Author = { S.I. Goldberg }, Title = { {H}armonic mappings of generalized dilation }, Booktitle = { {G}eometry {S}eminars. {S}essions on topology and geometry of manifolds }, Publisher = { University of Bologna }, Address = { Bologna }, Pages = { 39-53 }, Year = { 1992 } } @Article{ GolHar77, Author = { S.I. Goldberg and Z. Har'el }, Title = { {A} general {S}chwarz lemma for {R}iemannian manifolds }, Journal = { Bull.\ Soc.\ Math.\ Gr\`ece }, Volume = { 12 }, Pages = { 141-8 }, Year = { 1977 } } @Article{ GolHar79, Author = { S.I. Goldberg and Z. Har'el }, Title = { {M}appings of almost {H}ermitian manifolds }, Journal = { J. Differential Geom. }, Volume = { 14 }, Pages = { 67-80 }, Year = { 1979 } } @Article{ GolIsh76, Author = { S.I. Goldberg and T. Ishihara }, Title = { {H}armonic quasiconformal mappings of {R}iemannian manifolds }, Journal = { Amer.\ J. Math. }, Volume = { 98 }, Pages = { 225-240 }, Year = { 1976 } } @Article{ GolIsh78, Author = { S.I. Goldberg and T. Ishihara }, Title = { {R}iemannian submersions commuting with the {L}aplacian }, Journal = { J. Differential Geom. }, Volume = { 13 }, Pages = { 144-149 }, Year = { 1978 } } @Article{ GolIshPet74, Author = { S.I. Goldberg and T. Ishihara and N.C. Petridis }, Title = { {M}appings of bounded dilatation }, Journal = { J. Math.\ Tokushima Univ. }, Volume = { 8 }, Pages = { 1-7 }, Year = { 1974 } } @Article{ GolIshPet75, Author = { S.I. Goldberg and T. Ishihara and N.C. Petridis }, Title = { {M}appings of bounded dilatation of {R}iemannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 10 }, Pages = { 619-630 }, Year = { 1975 } } @Article{ GolMue82, Author = { S.I. Goldberg and C. Mueller }, Title = { {B}rownian motion, geometry, and generalizations of {P}icard's little theorem }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 7 }, Pages = { 259-263 }, Year = { 1982 } } @Article{ GolMue83, Author = { S.I. Goldberg and C. Mueller }, Title = { {B}rownian motion, geometry, and generalizations of {P}icard's little theorem }, Journal = { Ann.\ Probab. }, Volume = { 11 }, Pages = { 833-846 }, Year = { 1983 } } @Incollection{ GolTot87, Author = { S.I. Goldberg and G. Toth }, Title = { {R}emarks on {W}ente's example of an immersed torus in {${E}^3$} }, Booktitle = { {D}iff. {G}eom. and {A}ppl. {B}rno }, Publisher = { Reidel }, Address = { Dordrecht }, Pages = { 71-78 }, Year = { 1987 } } @Article{ GolTot89, Author = { S.I. Goldberg and G. Toth }, Title = { {O}n closed surfaces immersed in {${E}^3$} with constant mean curvature }, Journal = { J. London Math.\ Soc. }, Volume = { 38 }, Pages = { 333-340 }, Year = { 1989 } } @Article{ Gol72, Author = { R.A. Goldstein }, Title = { {S}tability of the boundary-value problem for harmonic mappings }, Journal = { J. Math.\ Anal.\ Appl. }, Volume = { 39 }, Pages = { 346-359 }, Year = { 1972 } } @Article{ Gor72, Author = { W.B. Gordon }, Title = { {C}onvex functions and harmonic maps }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 33 }, Pages = { 433-437 }, Year = { 1972 } } @Article{ Gor92, Author = { C. Gorodski }, Title = { {C}losed minimal hypersurfaces in compact symmetric spaces }, Journal = { Internat.\ J. Math. }, Volume = { 3 }, Pages = { 629-651 }, Year = { 1992 } } @Article{ Gor94, Author = { C. Gorodski }, Title = { {M}inimal sphere bundles in {E}uclidean spheres }, Journal = { Geom.\ Dedicata }, Volume = { 53 }, Pages = { 75-102 }, Year = { 1994 } } @Article{ Gor88, Author = { V.P. Gorokh }, Title = { {E}xistence of {$2$}-dimensional minimal surfaces in {${E}^4$} }, Journal = { Ukrain.\ Geom.\ Sb. }, Volume = { 31 }, Pages = { 36-47 }, Year = { 1988 } } @Article{ Gor89, Author = { V.P. Gorokh }, Title = { {M}inimal surfaces of constant {G}auss curvature in a pseudo-{R}iemannian sphere }, Journal = { Ukrain.\ Geom.\ Sb. }, Volume = { 32 }, Pages = { 27-34 }, Year = { 1989 } } @Unpublished{ Got95, Author = { T. Gotoh }, Title = { {C}ompact minimal {C}{R}-submanifolds with the least nullity in a complex projective space }, Note = { Preprint }, Year = { 1995 } } @Article{ Gra82, Author = { S. Granlund }, Title = { {A}n {${L}^p$}-estimate for the gradients of extremals }, Journal = { Math.\ Scand. }, Volume = { 50 }, Pages = { 66-72 }, Year = { 1982 } } @Article{ GraLinMar83, Author = { S. Granlund and P. Linqvist and O. Martio }, Title = { {C}onformally invariant variational integrals }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 277 }, Pages = { 43-73 }, Year = { 1983 } } @Article{ Gra89, Author = { J. Gravesen }, Title = { {O}n the topology of spaces of holomorphic maps }, Journal = { Acta Math. }, Volume = { 62 }, Pages = { 247-286 }, Year = { 1989 } } @Article{ Gra90, Author = { J. Gravesen }, Title = { {L}oop groups and {Y}ang {M}ills theory in dimension {$2$} }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 127 }, Pages = { 597-605 }, Year = { 1990 } } @Incollection{ Gra82A, Author = { A. Gray }, Title = { {V}ector cross products, harmonic maps and the {C}auchy--{R}iemann equations }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 57-74 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ Gra, Author = { M. Grayson }, Title = { {T}he shape of a figure-eight under the curve shortening flow }, Journal = { Invent.\ Math. } } @Article{ Gra87, Author = { M. Grayson }, Title = { {T}he heat equation shrinks embedded plane curves to round points }, Journal = { J. Differential Geom. }, Volume = { 26 }, Pages = { 285-314 }, Year = { 1987 } } @Article{ Gra89A, Author = { M. Grayson }, Title = { {S}hortening embedded curves }, Journal = { Ann.\ of Math. }, Volume = { 129 }, Pages = { 71-111 }, Year = { 1989 } } @Article{ Gra89B, Author = { M. Grayson }, Title = { {A} short note on the evolution of a surface by its mean curvature }, Journal = { Duke Math.\ J. }, Volume = { 58 }, Pages = { 555-558 }, Year = { 1989 } } @Misc{ GraHam, Author = { M. Grayson and R.S. Hamilton }, Title = { {T}he formation of singularities in the harmonic map heat flow } } @Article{ Gre93, Author = { C. Greco }, Title = { {T}he {D}irichlet problem for harmonic maps from the disc into a {L}orentzian warped product }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 10 }, Pages = { 239-252 }, Year = { 1993 } } @Article{ Gre78, Author = { M.L. Green }, Title = { {H}olomorphic maps to complex tori }, Journal = { Amer.\ J. Math. }, Volume = { 100 }, Pages = { 615-620 }, Year = { 1978 } } @Article{ GreShi81, Author = { R.E. Greene and K. Shiohama }, Title = { {C}onvex functions on complete noncompact manifolds: {D}ifferentiable structure }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 14 }, Pages = { 357-367 }, Year = { 1981 } } @Article{ GreShi81A, Author = { R.E. Greene and K. Shiohama }, Title = { {C}onvex functions on complete noncompact manifolds: {T}opological structure }, Journal = { Invent.\ Math. }, Volume = { 63 }, Pages = { 129-157 }, Year = { 1981 } } @Article{ GreWu73, Author = { R.E. Greene and H.H. Wu }, Title = { {O}n the subharmonicity and plurisubharmonicity of geodesically convex functions }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 22 }, Pages = { 641-653 }, Year = { 1973 } } @Article{ GreWu74, Author = { R.E. Greene and H.H. Wu }, Title = { {I}ntegrals of subharmonic functions on manifolds of nonnegative curvature }, Journal = { Invent.\ Math. }, Volume = { 27 }, Pages = { 265-298 }, Year = { 1974 } } @Article{ GreWu75, Author = { R.E. Greene and H.H. Wu }, Title = { {E}mbedding of open {R}iemannian manifolds by harmonic functions }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 25 }, Pages = { 215-235 }, Year = { 1975 } } @Article{ GreWu76, Author = { R.E. Greene and H.H. Wu }, Title = { {${C}^{\infty}$} convex functions and manifolds of positive curvature }, Journal = { Acta Math. }, Volume = { 137 }, Pages = { 209-245 }, Year = { 1976 } } @Incollection{ GreWu77, Author = { R.E. Greene and H.H. Wu }, Title = { {A}nalysis on noncompact {K}\"ahler manifolds }, Booktitle = { {S}everal {C}omplex {V}ariables }, Editor = { R.O. Wells }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 30 }, Pages = { 69-100 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1977 } } @Article{ GreWu79, Author = { R.E. Greene and H.H. Wu }, Title = { {${C}^{\infty}$} approximations of convex, subharmonic, and plurisubharmonic functions }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 12 }, Pages = { 47-84 }, Year = { 1979 } } @Book{ GreWu79A, Author = { R.E. Greene and H.H. Wu }, Title = { {F}unction theory on manifolds which possess a pole }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 699 }, Series = { Lecture Notes in Math. }, Year = { 1979 } } @Article{ GreWu81, Author = { R.E. Greene and H.H. Wu }, Title = { {H}armonic forms on noncompact {R}iemannian and {K}\"ahler manifolds }, Journal = { Michigan Math.\ J. }, Volume = { 28 }, Pages = { 63-81 }, Year = { 1981 } } @Book{ Gri76, Author = { P.A. Griffiths }, Title = { {E}ntire holomorphic mappings in one and several complex variables }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 85 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1976 } } @Article{ GriHar79, Author = { P.A. Griffiths and J. Harris }, Title = { {A}lgebraic geometry and local differential geometry }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 12 }, Pages = { 355-432 }, Year = { 1979 } } @Misc{ Gri, Author = { A.A. Grigoryan }, Title = { {H}eat kernel on a non-compact {R}iemannian manifold } } @Article{ Gri87, Author = { A.A. Grigoryan }, Title = { {A} criterion for the existence on a {R}iemannian manifold of a nontrivial bounded harmonic function with finite {D}irichlet integral }, Journal = { Soviet Math.\ Dokl. }, Volume = { 35 }, Pages = { 339-341 }, Year = { 1987 } } @Article{ Gro85, Author = { M. Gromov }, Title = { {P}seudo holomorphic curves in symplectic manifolds }, Journal = { Invent.\ Math. }, Volume = { 82 }, Pages = { 307-347 }, Year = { 1985 } } @Article{ Gro91, Author = { M. Gromov }, Title = { {F}oliated {P}lateau problem. {I}. {M}inimal varieties }, Journal = { Geom.\ Funct.\ Anal. }, Volume = { 1 }, Pages = { 14-79 }, Year = { 1991 } } @Article{ Gro91A, Author = { M. Gromov }, Title = { {F}oliated {P}lateau problem. {I}{I}. {H}armonic maps of foliations }, Journal = { Geom.\ Funct.\ Anal. }, Volume = { 1 }, Pages = { 253-320 }, Year = { 1991 } } @Article{ Gro94, Author = { M. Gromov }, Title = { {S}ign and geometric meaning of curvature }, Journal = { Rend.\ Sem.\ Mat.\ Fis.\ Milano }, Volume = { 61 }, Pages = { 9-123 }, Year = { 1994 } } @Article{ GroSch92, Author = { M. Gromov and R. Schoen }, Title = { {H}armonic maps into singular spaces and {$p$}-adic superrigidity for lattices in groups of rank one }, Journal = { Inst.\ Hautes \'Etudes Sci.\ Publ.\ Math. }, Volume = { 76 }, Pages = { 165-246 }, Year = { 1992 } } @Article{ Gro92, Author = { K. Grosse-Brauchmann }, Title = { {I}nterior and boundary monotonicity formulas for stationary harmonic maps }, Journal = { Manuscripta Math. }, Volume = { 77 }, Pages = { 89-95 }, Year = { 1992 } } @Article{ Gro93, Author = { K. Grosse-Brauchmann }, Title = { {N}ew surfaces of constant mean curvature }, Journal = { Math.\ Z. }, Volume = { 214 }, Pages = { 527-565 }, Year = { 1993 } } @Unpublished{ Gro95, Author = { K. Grosse-Brauckmann }, Title = { {S}table constant mean curvature surfaces minimize area }, Note = { SFB 256 preprint }, Year = { 1995 } } @Misc{ Gro, Author = { J.F. Grotowski }, Title = { {P}artial and full regularity for restricted classes of {$p$}-harmonic maps } } @Article{ Gro91B, Author = { J.F. Grotowski }, Title = { {H}armonic map heat flow for axially symmetric data }, Journal = { Manuscripta Math. }, Volume = { 73 }, Pages = { 207-228 }, Year = { 1991 } } @Incollection{ Gro91C, Author = { J.F. Grotowski }, Title = { {H}eat flow for harmonic maps }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 129-140 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Article{ Gro93A, Author = { J.F. Grotowski }, Title = { {C}oncentrated boundary data and axially symmetric harmonic maps }, Journal = { J. Geom.\ Anal. }, Volume = { 3 }, Pages = { 279-292 }, Year = { 1993 } } @Article{ Gro93B, Author = { J.F. Grotowski }, Title = { {F}inite time blow-up for the harmonic map heat flow }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 231--236 }, Year = { 1993 } } @Article{ Gro96, Author = { J.F. Grotowski }, Title = { {B}oundary value problems for energy minimizing harmonic maps }, Journal = { S{\^u}rikaisekikenky{\^u}sho K{\^o}ky{\^u}roku }, Volume = { 951 }, Pages = { 155--160 }, Note = { (Japanese) }, Year = { 1996 } } @Incollection{ Gro96A, Author = { J.F. Grotowski }, Title = { {E}quivariant harmonic maps and pendulum type equations }, Booktitle = { {P}rogress in partial differential equations: the {M}etz surveys }, Publisher = { Longman }, Address = { Harlow }, Volume = { 345 }, Pages = { 83-91 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1996 } } @Article{ GroSheYan95, Author = { J.F. Grotowski and Y. Shen and S. Yan }, Title = { {O}n various classes of harmonic maps }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 64 }, Pages = { 353-358 }, Year = { 1995 } } @Article{ GruKovSus95, Author = { A.M. Grundland and M. Kovalyov and M. Sussman }, Title = { {O}n the behavior of some explicit solutions of the harmonic maps equation }, Journal = { Rocky Mountain J. Math. }, Volume = { 25 }, Pages = { 231-347 }, Year = { 1995 } } @Unpublished{ Gru, Author = { M. Gr{\"u}ter }, Title = { {A} remark on isolated singularites at the free boundary of harmonic maps }, Note = { Bonn preprint } } @Unpublished{ Gru78, Author = { M. Gr{\"u}ter }, Title = { {E}in {H}ebbarkeitsatz f\"ur isolierte {S}ingularit\"aten }, Note = { Bonn preprint }, Year = { 1978 } } @Article{ Gru81, Author = { M. Gr{\"u}ter }, Title = { {R}egularity of weak {${H}$}-surfaces }, Journal = { J. Reine Angew.\ Math. }, Volume = { 329 }, Pages = { 1-15 }, Year = { 1981 } } @Unpublished{ Gru82, Author = { M. Gr{\"u}ter }, Title = { {A} note on variational integrals which are conformally invariant }, Note = { SFB 72, Bonn }, Year = { 1982 } } @Article{ Gru84, Author = { M. Gr{\"u}ter }, Title = { {C}onformally invariant variational integrals and the removability of isolated singularities }, Journal = { Manuscripta Math. }, Volume = { 47 }, Pages = { 85-104 }, Year = { 1984 } } @Unpublished{ Gru85, Author = { M. Gr{\"u}ter }, Title = { {O}ptimal regularity for codimension one minimal surfaces with a free boundary }, Note = { Bonn preprint }, Year = { 1985 } } @Unpublished{ Gru85A, Author = { M. Gr{\"u}ter }, Title = { {R}egularity results for minimizing currents with a free boundary }, Note = { Bonn preprint }, Year = { 1985 } } @Article{ Gru86, Author = { M. Gr{\"u}ter }, Title = { {E}ine {B}emerkung zur {R}egularit\"at station\"arer {P}unkte von konform invarianten {V}ariationsintegralen }, Journal = { Manuscripta Math. }, Volume = { 55 }, Pages = { 451-453 }, Year = { 1986 } } @Unpublished{ Gru90, Author = { M. Gr{\"u}ter }, Title = { {G}eometric measure theory and minimal surfaces }, Note = { Bonn preprint }, Year = { 1990 } } @Article{ Gru97, Author = { M. Gr{\"u}ter }, Title = { {A} remark on isolated singularities at the free boundary of harmonic maps }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 15 }, Pages = { 173--178 }, Year = { 1997 } } @Article{ GruHilNit81, Author = { M. Gr{\"u}ter and S. Hildebrandt and J.C.C. Nitsche }, Title = { {O}n the boundary behavior of minimal surfaces with a free boundary which are not minima of the area }, Journal = { Manuscripta Math. }, Volume = { 35 }, Pages = { 387-410 }, Year = { 1981 } } @Unpublished{ GruHilNit84, Author = { M. Gr{\"u}ter and S. Hildebrandt and J.C.C. Nitsche }, Title = { {R}egularity for stationary surfaces of constant mean curvature with free boundaries }, Note = { SFB 72, Bonn }, Year = { 1984 } } @Misc{ GruJos, Author = { M. Gr{\"u}ter and J. Jost }, Title = { {A}llard type regularity results for varifolds with free boundaries } } @Article{ GruJos86, Author = { M. Gr{\"u}ter and J. Jost }, Title = { {O}n embedded minimal discs in convex bodies }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 3 }, Pages = { 345-390 }, Year = { 1986 } } @Unpublished{ Gu, Author = { C.H. Gu }, Title = { {A} global study of extremal surfaces in {$3$}-dimensional {M}inkowski space }, Note = { Fudan preprint } } @Misc{ GuA, Author = { C.H. Gu }, Title = { {H}armonic maps of manifolds with indefinite metric } } @Article{ Gu80, Author = { C.H. Gu }, Title = { {O}n the {C}auchy problem for harmonic maps defined on two-dimensional {M}inkowski space }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 33 }, Pages = { 727-737 }, Year = { 1980 } } @Article{ Gu80A, Author = { C.H. Gu }, Title = { {O}n the initial-boundary value problem for harmonic maps from the {$2$}-dimensional {M}inkowski space }, Journal = { Manuscripta Math. }, Volume = { 33 }, Pages = { 51-58 }, Year = { 1980 } } @Incollection{ Gu83, Author = { C.H. Gu }, Title = { {O}n the motion of a string in a curved space-time }, Booktitle = { {P}roc. {T}hird {M}. {G}rossmann meeting }, Publisher = { North Holland }, Pages = { 139-142 }, Year = { 1983 } } @Incollection{ Gu83A, Author = { C.H. Gu }, Title = { {S}ome problems on non-linear hyperbolic systems }, Booktitle = { {P}roc. 1980 {B}eijing {S}ymposium. {D}ifferential {G}eometry and {D}ifferential {E}quations, {V}ol. 1 }, Publisher = { Gordon and Breach }, Pages = { 467-479 }, Year = { 1983 } } @Article{ Gu84, Author = { C.H. Gu }, Title = { {O}n the harmonic maps from {${\bf {R}}^{1,1}$} to {${S}^{1,1}$} }, Journal = { J. Reine Angew.\ Math. }, Volume = { 346 }, Pages = { 101-109 }, Year = { 1984 } } @Article{ Gu85, Author = { C.H. Gu }, Title = { {T}he extremal surfaces in the {$3$}-dimensional {M}inkowski space }, Journal = { Acta Math.\ Sinica (N.S.) }, Volume = { 1 }, Pages = { 171-180 }, Year = { 1985 } } @Article{ GuHu86, Author = { C.H. Gu and H.S. Hu }, Title = { {S}ome developments of harmonic maps }, Journal = { Adv.\ in Sci.\ of China }, Volume = { 1 }, Pages = { 109-127 }, Year = { 1986 } } @Article{ GuHu95, Author = { C.H. Gu and H.S. Hu }, Title = { {E}xplicit construction of harmonic maps from {${\bf {R}}^2$} to {${U}({N})$} }, Journal = { Chinese Ann.\ Math. }, Volume = { 16B }, Pages = { 139-152 }, Year = { 1995 } } @Article{ GuaTri85, Author = { I.V. Guadalupe and R. Tribuzy }, Title = { {M}inimal immersions of surfaces into {$4$}-dimensional space forms }, Journal = { Rend.\ Sem.\ Mat.\ Univ.\ Padova }, Volume = { 73 }, Pages = { 1-13 }, Year = { 1985 } } @Incollection{ GuaGutSot, Author = { I. Guadalupe and C. Gutierrez and J. Sotomayor and R. Tribuzy }, Title = { {P}rincipal lines on surfaces minimally immersed in constantly curved {$4$}-spaces }, Booktitle = { {D}ynamical {S}ystems and {B}ifurcation {T}heory }, Editor = { M.I. Camacho and M.J. Pacifico and F. Takens }, Publisher = { Longman }, Address = { Harlow }, Volume = { 160 }, Pages = { 91-120 }, Series = { Pitman Res.\ Notes Math.\ Ser. } } @Misc{ GuaSpr, Author = { B. Guan and J. Spruck }, Title = { {B}oundary value problems on {${S}^n$} for surfaces of constant {G}auss curvature } } @Unpublished{ Gud, Author = { S. Gudmundsson }, Title = { {T}he geometry of harmonic morphisms }, Note = { PhD thesis, Leeds, 1992 } } @Article{ GudA, Author = { S. Gudmundsson }, Title = { {O}n the existence of harmonic morphisms from symmetric spaces of rank one }, Journal = { Manuscripta Math. }, Note = { (to appear) } } @Unpublished{ Gud88, Author = { S. Gudmundsson }, Title = { {H}armonische {$2$}-{S}ph\"aren in komplexen {G}rassmann-{M}annigfaltigkeiten }, Note = { Diplomarbeit Bonn }, Year = { 1988 } } @Article{ Gud90, Author = { S. Gudmundsson }, Title = { {O}n the geometry of harmonic morphisms }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 108 }, Pages = { 461-466 }, Year = { 1990 } } @Article{ Gud91, Author = { S. Gudmundsson }, Title = { {O}n the geometry of certain harmonic two-spheres in complex {G}rassmannians }, Journal = { Boll.\ Un.\ Mat.\ Ital. }, Volume = { 5 }, Pages = { 653-664 }, Year = { 1991 } } @Article{ Gud92, Author = { S. Gudmundsson }, Title = { {H}armonic morphisms between spaces of constant curvature }, Journal = { Proc.\ Edinburgh Math.\ Soc. }, Volume = { 36 }, Pages = { 133-143 }, Year = { 1992 } } @Article{ Gud94, Author = { S. Gudmundsson }, Title = { {H}armonic morphisms from complex projective spaces }, Journal = { Geom.\ Dedicata }, Volume = { 53 }, Pages = { 155-161 }, Year = { 1994 } } @Article{ Gud94A, Author = { S. Gudmundsson }, Title = { {N}on-holomorphic harmonic morphisms from {K}\"ahler manifolds }, Journal = { Manuscripta Math. }, Volume = { 85 }, Pages = { 67-78 }, Year = { 1994 } } @Article{ Gud95, Author = { S. Gudmundsson }, Title = { {H}armonic morphisms from quaternionic projective spaces }, Journal = { Geom.\ Dedicata }, Volume = { 56 }, Pages = { 327-332 }, Year = { 1995 } } @Article{ Gud96, Author = { S. Gudmundsson }, Title = { {M}inimal submanifolds of hyperbolic spaces via harmonic morphisms }, Journal = { Geom.\ Dedicata }, Volume = { 62 }, Pages = { 269-279 }, Year = { 1996 } } @Article{ Gud97, Author = { S. Gudmundsson }, Title = { {H}armonic morphisms as sphere bundles over compact {R}iemann surfaces }, Journal = { Internat.\ J. Math. }, Volume = { 8 }, Note = { (to appear) }, Year = { 1997 } } @Article{ GudSig93, Author = { S. Gudmundsson and R. Sigurdsson }, Title = { {A} note on the classification of holomorphic harmonic morphisms }, Journal = { Potential Analysis }, Volume = { 2 }, Pages = { 295-298 }, Year = { 1993 } } @Article{ GudWoo93, Author = { S. Gudmundsson and J.C. Wood }, Title = { {M}ultivalued harmonic morphisms }, Journal = { Math.\ Scand. }, Volume = { 73 }, Pages = { 127-155 }, Year = { 1993 } } @Article{ GudWoo97, Author = { S. Gudmundsson and J.C. Wood }, Title = { {H}armonic morphisms between almost {H}ermitian manifolds }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ B }, Volume = { 11 }, Pages = { 30-58 }, Year = { 1997 } } @Misc{ Gue, Author = { M.A. Guest }, Title = { {R}ecent developments concerning harmonic maps from {R}iemann surfaces into {L}ie groups } } @Article{ Gue84, Author = { M.A. Guest }, Title = { {T}opology of the space of absolute minima of the energy functional }, Journal = { Amer.\ J. Math. }, Volume = { 106 }, Pages = { 21-42 }, Year = { 1984 } } @Incollection{ Gue85, Author = { M.A. Guest }, Title = { {G}eodesics, harmonic maps and the {Y}ang--{M}ills equations }, Booktitle = { {T}opics in several complex variables }, Editor = { E. Ram{\'\i}rez~de~Arellano and D. Sundararaman }, Publisher = { Pitman }, Address = { London }, Volume = { 112 }, Pages = { 102-108 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Incollection{ Gue85A, Author = { M.A. Guest }, Title = { {I}nstantons and harmonic maps }, Booktitle = { {I}nfinite dimensional groups with applications }, Editor = { V. Kac }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 4 }, Pages = { 137-156 }, Series = { MSRI Publ. }, Year = { 1985 } } @Article{ Gue87, Author = { M.A. Guest }, Title = { {G}eometry of maps between generalized flag manifolds }, Journal = { J. Differential Geom. }, Volume = { 25 }, Pages = { 223-247 }, Year = { 1987 } } @Incollection{ Gue87A, Author = { M.A. Guest }, Title = { {O}rbits and harmonic maps }, Booktitle = { {T}he {L}efschetz centennial conference, {P}art {I}{I}{I}: {P}roceedings on {D}ifferential {E}quations }, Editor = { A. Verjovsky }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 58 }, Pages = { 161-171 }, Series = { Contemp.\ Math. }, Year = { 1987 } } @Incollection{ Gue88, Author = { M.A. Guest }, Title = { {T}he energy of harmonic maps obtained by the twistor construction }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 178-202 }, Year = { 1988 } } @Article{ Gue91, Author = { M.A. Guest }, Title = { {T}he energy function and homogeneous harmonic maps }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 62 }, Pages = { 77-98 }, Year = { 1991 } } @Article{ Gue92, Author = { M.A. Guest }, Title = { {H}armonic two-spheres in complex projective spaces and some open problems }, Journal = { Exposition.\ Math. }, Volume = { 10 }, Pages = { 61-87 }, Year = { 1992 } } @Article{ Gue92A, Author = { M.A. Guest }, Title = { {I}nstantons, rational maps and harmonic maps }, Journal = { Mat.\ Contemp. }, Volume = { 2 }, Pages = { 113-155 }, Year = { 1992 } } @Article{ Gue94, Author = { M.A. Guest }, Title = { {C}onfiguration spaces and the space of rational curves on a toric variety }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 31 }, Pages = { 191-196 }, Year = { 1994 } } @Article{ Gue94A, Author = { M.A. Guest }, Title = { {O}n the space of holomorphic maps from the {R}iemann sphere to the quadric cone }, Journal = { Quart.\ J. Math.\ Oxford }, Volume = { 45 }, Pages = { 57-75 }, Year = { 1994 } } @Article{ Gue95, Author = { M.A. Guest }, Title = { {T}he topology of the space of rational curves on a toric variety }, Journal = { Acta Math. }, Volume = { 174 }, Pages = { 119-145 }, Year = { 1995 } } @Book{ Gue97, Author = { M.A. Guest }, Title = { {H}armonic {M}aps, {L}oop {G}roups, and {I}ntegrable {S}ystems, }, Publisher = { Cambridge University Press }, Address = { Cambridge }, Year = { 1997 } } @Article{ GueOhn93, Author = { M.A. Guest and Y. Ohnita }, Title = { {G}roup actions and deformations for harmonic maps }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 45 }, Pages = { 671-704 }, Year = { 1993 } } @Article{ GueOhn94, Author = { M.A. Guest and Y. Ohnita }, Title = { {A}ctions of loop groups, deformations of harmonic maps, and their applications }, Journal = { Sugaku }, Volume = { 46 }, Pages = { 228-242 }, Year = { 1994 } } @Incollection{ GueOhn94A, Author = { M.A. Guest and Y. Ohnita }, Title = { {L}oop group actions on harmonic maps and their applications }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 273-292 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ GuePre88, Author = { M.A. Guest and A.N. Pressley }, Title = { {H}olomorphic curves in loop groups }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 118 }, Pages = { 511-527 }, Year = { 1988 } } @Article{ GuiKaz80, Author = { V. Guillemin and D. Kazhdan }, Title = { {S}ome inverse spectral results for negatively curved {$2$}-manifolds }, Journal = { Topology }, Volume = { 19 }, Pages = { 301-312 }, Year = { 1980 } } @Article{ GuiKosSte88, Author = { V. Guillemin and B. Kostant and S. Sternberg }, Title = { {D}ouglas' solution of the {P}lateau problem }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 85 }, Pages = { 3277-3278 }, Year = { 1988 } } @Incollection{ Gul, Author = { R. Gulliver }, Title = { {M}inimal surfaces of finite index in manifolds of positive scalar curvature }, Booktitle = { {C}alculus of variations and partial differential equations ({C}.{I}.{R}.{M}.) }, Note = { (to appear) } } @Article{ Gul72, Author = { R. Gulliver }, Title = { {S}urfaces of constant mean curvature which have a simple projection }, Journal = { Math.\ Z. }, Volume = { 129 }, Pages = { 95-107 }, Year = { 1972 } } @Article{ Gul73, Author = { R. Gulliver }, Title = { {E}xistence of surfaces with prescribed mean curvature vector }, Journal = { Math.\ Z. }, Volume = { 131 }, Pages = { 117-140 }, Year = { 1973 } } @Article{ Gul73A, Author = { R. Gulliver }, Title = { {T}he {P}lateau problem for surfaces of prescribed mean curvature in a {R}iemannian manifold }, Journal = { J. Differential Geom. }, Volume = { 8 }, Pages = { 317-330 }, Year = { 1973 } } @Article{ Gul73B, Author = { R. Gulliver }, Title = { {R}egularity of minimizing surfaces of prescribed mean curvature }, Journal = { Ann.\ of Math. }, Volume = { 97 }, Pages = { 275-305 }, Year = { 1973 } } @Article{ Gul74, Author = { R. Gulliver }, Title = { {O}n the nonexistence of a hypersurface of prescribed mean curvature with a given boundary }, Journal = { Manuscripta Math. }, Volume = { 11 }, Pages = { 15-39 }, Year = { 1974 } } @Article{ Gul75, Author = { R. Gulliver }, Title = { {B}ranched immersions of surfaces and reduction of topological type, {I} }, Journal = { Math.\ Z. }, Volume = { 145 }, Pages = { 267-288 }, Year = { 1975 } } @Article{ Gul75A, Author = { R. Gulliver }, Title = { {O}n the variety of manifolds without conjugate }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 210 }, Pages = { 185-201 }, Year = { 1975 } } @Article{ Gul76, Author = { R. Gulliver }, Title = { {F}initeness of the ramified set for branched immersions of surfaces }, Journal = { Pacific J. Math. }, Volume = { 64 }, Pages = { 153-165 }, Year = { 1976 } } @Article{ Gul76A, Author = { R. Gulliver }, Title = { {R}emovability of singular points on surfaces of bounded mean curvature }, Journal = { J. Differential Geom. }, Volume = { 11 }, Pages = { 345-350 }, Year = { 1976 } } @Article{ Gul77, Author = { R. Gulliver }, Title = { {B}ranched immersions of surfaces and reduction of topological type, {I}{I} }, Journal = { Math.\ Ann. }, Volume = { 230 }, Pages = { 25-48 }, Year = { 1977 } } @Incollection{ Gul83, Author = { R. Gulliver }, Title = { {N}ecessary conditions for submanifolds and currents with prescribed mean curvature vector }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, N.J. }, Volume = { 103 }, Pages = { 225-242 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Incollection{ Gul86, Author = { R. Gulliver }, Title = { {I}ndex and total curvature of complete minimal surfaces }, Booktitle = { {G}eometric measure theory and the calculus of variations }, Editor = { W.K. Allard and F.J. Almgren }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 44 }, Pages = { 207-211 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Unpublished{ Gul86A, Author = { R. Gulliver }, Title = { {M}inimal surfaces of finite index in manifolds of positive scalar curvature }, Note = { SFB72, Bonn }, Year = { 1986 } } @Unpublished{ Gul89, Author = { R. Gulliver }, Title = { {C}onvergence of minimal submanifolds to a singular variety }, Note = { SFB256, Bonn }, Year = { 1989 } } @Incollection{ Gul91, Author = { R. Gulliver }, Title = { {F}iber evolution in the heat flow of harmonic maps }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 173-178 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Incollection{ Gul91A, Author = { R. Gulliver }, Title = { {H}armonic mappings, symmetry and computer graphics }, Booktitle = { {G}eometric {A}nalysis and {C}omputer {G}raphics }, Editor = { P. Concus and R. Finn and D.A. Hoffman }, Publisher = { Springer }, Address = { Berlin }, Volume = { 17 }, Pages = { 79-87 }, Series = { MSRI Publ. }, Year = { 1991 } } @Article{ GulHil86, Author = { R. Gulliver and S. Hildebrandt }, Title = { {B}oundary configurations spanning continua of minimal surfaces }, Journal = { Manuscripta Math. }, Volume = { 54 }, Pages = { 323-347 }, Year = { 1986 } } @Article{ GulJos87, Author = { R. Gulliver and J. Jost }, Title = { {H}armonic maps which solve a free boundary problem }, Journal = { J. Reine Angew.\ Math. }, Volume = { 381 }, Pages = { 61-89 }, Year = { 1987 } } @Incollection{ GulLaw86, Author = { R. Gulliver and H.B. Lawson }, Title = { {T}he structure of stable minimal hypersurfaces near a singularity }, Booktitle = { {G}eometric measure theory and the calculus of variations }, Editor = { W.K. Allard and F.J. Almgren }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 44 }, Pages = { 213-237 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Article{ GulLes73, Author = { R. Gulliver and F.D. Lesley }, Title = { {O}n boundary branch points of minimizing surfaces }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 52 }, Pages = { 20-25 }, Year = { 1973 } } @Article{ GulOssRoy73, Author = { R. Gulliver and R. Osserman and H.L. Royden }, Title = { {A} theory of branched immersions of surfaces }, Journal = { Amer.\ J. Math. }, Volume = { 95 }, Pages = { 750-812 }, Year = { 1973 } } @Article{ GulSpr71, Author = { R. Gulliver and J. Spruck }, Title = { {T}he {P}lateau problem for surfaces of prescribed mean curvature in a cylinder }, Journal = { Invent.\ Math. }, Volume = { 13 }, Pages = { 169-178 }, Year = { 1971 } } @Article{ GulSpr72, Author = { R. Gulliver and J. Spruck }, Title = { {E}xistence theorems for parametric surface of prescribed mean curvature }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 22 }, Pages = { 445-472 }, Year = { 1972 } } @Article{ GulSpr72A, Author = { R. Gulliver and J. Spruck }, Title = { {S}urfaces of constant mean curvature which have a simple projection }, Journal = { Math.\ Z. }, Volume = { 129 }, Pages = { 95-107 }, Year = { 1972 } } @Article{ GulSpr76, Author = { R. Gulliver and J. Spruck }, Title = { {O}n embedded minimal surfaces }, Journal = { Ann.\ of Math. }, Volume = { 103 }, Pages = { 331-347 }, Year = { 1976 } } @Article{ GulTom89, Author = { R. Gulliver and F. Tomi }, Title = { {O}n false branch points of incompressible branched immersions }, Journal = { Manuscripta Math. }, Volume = { 63 }, Pages = { 293-302 }, Year = { 1989 } } @Article{ GulWhi89, Author = { R. Gulliver and B. White }, Title = { {T}he rate of convergence of a harmonic map at a singular point }, Journal = { Math.\ Ann. }, Volume = { 283 }, Pages = { 539-549 }, Year = { 1989 } } @Incollection{ GulWhi91, Author = { R. Gulliver and B. White }, Title = { {O}n convergence rates of harmonic maps near points of discontinuity }, Booktitle = { {C}oll\`ege de {F}rance, {S}eminar {V}ol.{X}. }, Publisher = { Longman }, Address = { Harlow }, Volume = { 220 }, Pages = { 216-228 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1991 } } @Article{ GuoHon93, Author = { B.L. Guo and M.C. Hong }, Title = { {T}he {L}andau--{L}ifschitz equation of the ferromagnetic spin chain and harmonic maps }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 311-334 }, Year = { 1993 } } @Article{ GuoWan96, Author = { B.L. Guo and Y. Wang }, Title = { {G}eneralized {L}andau-{L}ifshitz systems and harmonic maps }, Journal = { Sci.\ China Ser.\ A }, Volume = { 39 }, Pages = { 1242--1257 }, Year = { 1996 } } @Article{ Guo81, Author = { H.Y. Guo }, Title = { {G}auge theory and functional harmonic mapping }, Journal = { Acta Math.\ Sci. }, Volume = { 1 }, Pages = { 257-259 }, Year = { 1981 } } @Article{ Guo82, Author = { H.Y. Guo }, Title = { {M}odels of harmonic mapping theory for the {B}eltrami space-time of constant curvature }, Journal = { Kexue Tongbao }, Volume = { 27 }, Pages = { 24-26 }, Year = { 1982 } } @Article{ Guo96, Author = { R. Guo }, Title = { {S}ome remarks on orthogonal multiplication }, Journal = { Acta Sci.\ Natur.\ Univ.\ Norm.\ Hunan. }, Volume = { 19 }, Pages = { 7--10 }, Year = { 1996 } } @Article{ GurJanXan83, Author = { M. G{\"u}rses and R. Jantzen and B.C. Xanthopoulos }, Title = { {H}armonic mappings and {${S}{U}({N})$} self-dual {Y}ang--{M}ills fields }, Journal = { J. Phys.\ A }, Volume = { 16 }, Pages = { L635-L637 }, Year = { 1983 } } @Article{ GurTze80, Author = { F. G{\"u}rsey and H.C. Tze }, Title = { {C}omplex and quaternionic analyticity in chiral and gauge theories, {I} }, Journal = { Ann.\ Physics }, Volume = { 128 }, Pages = { 29-130 }, Year = { 1980 } } @Article{ GoeSim87, Author = { C.C. G{\'o}es and P.A.Q. Sim{\~o}es }, Title = { {T}he generalized {G}auss map of minimal surfaces in {${H}^3$} and {${H}^4$} }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 18 }, Pages = { 35-47 }, Year = { 1987 } } @Misc{ Hah, Author = { J. Hahn }, Title = { {I}soparametric hypersurfaces in the pseudo-{R}iemannian space forms } } @Article{ HalNut77, Author = { M. Halil and Y. Nutku }, Title = { {C}olliding impulsive gravitational waves }, Journal = { Phys.\ Rev.\ Lett. }, Volume = { 39 }, Pages = { 1379-1382 }, Year = { 1977 } } @Misc{ Hal, Author = { P. Hall }, Title = { {R}egular homotopies of branched immersions } } @Misc{ HalA, Author = { P. Hall }, Title = { {U}niqueness theorems for holomorphic curves } } @Unpublished{ Hal83, Author = { P. Hall }, Title = { {T}opological properties of minimal surfaces }, Note = { Warwick Thesis }, Year = { 1983 } } @Article{ Hal89, Author = { P. Hall }, Title = { {A} {P}icard theorem with an application to minimal surfaces {I} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 314 }, Pages = { 597-603 }, Year = { 1989 } } @Article{ Hal91, Author = { P. Hall }, Title = { {A} {P}icard theorem with an application to minimal surfaces {I}{I} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 325 }, Pages = { 895-902 }, Year = { 1991 } } @Unpublished{ Ham, Author = { R.S. Hamilton }, Title = { {E}ternal solutions to the mean curvature flow }, Note = { preprint } } @Unpublished{ HamA, Author = { R.S. Hamilton }, Title = { {A}n isoperimetric estimate for the {R}icci flow on the two-sphere }, Note = { preprint } } @Unpublished{ HamB, Author = { R.S. Hamilton }, Title = { {I}soperimetric estimates for the curve shrinking flow in the plane }, Note = { preprint } } @Misc{ HamC, Author = { R.S. Hamilton }, Title = { {W}orn stones with flat sides } } @Book{ Ham75, Author = { R.S. Hamilton }, Title = { {H}armonic maps of manifolds with boundary }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 471 }, Series = { Lecture Notes in Math. }, Year = { 1975 } } @Article{ Ham82, Author = { R.S. Hamilton }, Title = { {T}hree-manifolds with positive {R}icci curvature }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 255-306 }, Year = { 1982 } } @Incollection{ Ham84, Author = { R.S. Hamilton }, Title = { {T}he {R}icci curvature equation }, Booktitle = { {S}eminar on nonlinear partial differential equations }, Editor = { S.S. Chern }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 2 }, Pages = { 47-72 }, Series = { MSRI Publ. }, Year = { 1984 } } @Article{ Ham86, Author = { R.S. Hamilton }, Title = { {F}our-manifolds with positive curvature operator }, Journal = { J. Differential Geom. }, Volume = { 24 }, Pages = { 153-179 }, Year = { 1986 } } @Incollection{ Ham88, Author = { R.S. Hamilton }, Title = { {T}he {R}icci flow on surfaces }, Booktitle = { {M}athematics and general relativity }, Editor = { J.A. Isenberg }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 71 }, Pages = { 237-262 }, Series = { Contemp.\ Math. }, Year = { 1988 } } @Article{ Ham93, Author = { R.S. Hamilton }, Title = { {E}ternal solutions to the {R}icci flow }, Journal = { J. Differential Geom. }, Volume = { 38 }, Pages = { 1-11 }, Year = { 1993 } } @Article{ Ham93A, Author = { R.S. Hamilton }, Title = { {T}he {H}arnack estimate for the {R}icci flow }, Journal = { J. Differential Geom. }, Volume = { 37 }, Pages = { 225-243 }, Year = { 1993 } } @Article{ Ham93B, Author = { R.S. Hamilton }, Title = { {A} matrix {H}arnack estimate for the heat equation }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 113-126 }, Year = { 1993 } } @Article{ Ham93C, Author = { R.S. Hamilton }, Title = { {M}onotonicity formulae for parabolic flows on manifolds }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 127-137 }, Year = { 1993 } } @Article{ Ham95, Author = { R.S. Hamilton }, Title = { {A} compactness property for solutions of the {R}icci flow }, Journal = { Amer.\ J. Math. }, Volume = { 117 }, Pages = { 545-572 }, Year = { 1995 } } @Article{ Ham95A, Author = { R.S. Hamilton }, Title = { {H}arnack estimate for the mean curvature flow }, Journal = { J. Differential Geom. }, Volume = { 41 }, Pages = { 215-226 }, Year = { 1995 } } @Incollection{ Han96, Author = { Z.C. Han }, Title = { {R}emarks on the geometric behavior of harmonic maps between surfaces }, Booktitle = { {E}lliptic and parabolic methods in geometry ({M}inneapolis, {M}{N}, 1994) }, Publisher = { A.K. Peters }, Address = { Wellesley, MA }, Pages = { 57--66 }, Year = { 1996 } } @Misc{ HanTamTre, Author = { Z.C. Han and L.F. Tam and A. Treiberg and T. Wan }, Title = { {H}armonic maps from the complex plane into surfaces with nonpositive curvature } } @Article{ Han82, Author = { T. Hangan }, Title = { {V}ariational problems connected with tensor fields }, Journal = { Rend.\ Sem.\ Fac.\ Sci.\ Univ.\ Cagliari }, Volume = { 52 }, Pages = { 23-33 }, Year = { 1982 } } @Article{ HanSch85, Author = { W. Hangartner and G. Schober }, Title = { {U}nivalent harmonic mappings onto parallel slit domains }, Journal = { Michigan Math.\ J. }, Volume = { 32 }, Pages = { 131-134 }, Year = { 1985 } } @Article{ HanNom84, Author = { J. Hano and K. Nomizu }, Title = { {S}urfaces of revolution with constant mean curvature in {L}orentz-{M}inkowski space }, Journal = { T\^ohoku Math.\ J. }, Volume = { 36 }, Pages = { 427-437 }, Year = { 1984 } } @Article{ Har76, Author = { Z. Har'el }, Title = { {H}armonic maps and distorsion theorems }, Journal = { Tensor (N.S.) }, Volume = { 30 }, Pages = { 47-54 }, Year = { 1976 } } @Article{ Har78, Author = { Z. Har'el }, Title = { {H}armonic mappings of negatively curved manifolds }, Journal = { Canad.\ Math.\ Soc.\ J. }, Volume = { 30 }, Pages = { 631-637 }, Year = { 1978 } } @Article{ HarIsh88, Author = { F. Hara and T. Ishihara }, Title = { {S}urfaces of revolution in the {L}orentzian {$3$}-space }, Journal = { J. Math.\ Tokushima Univ. }, Volume = { 22 }, Pages = { 1-13 }, Year = { 1988 } } @Misc{ Har, Author = { R. Hardt }, Title = { {S}paces of harmonic maps with fixed singular sets } } @Unpublished{ HarA, Author = { R. Hardt }, Title = { {S}paces of harmonic maps with singular sets }, Note = { preprint } } @Incollection{ Har86, Author = { R. Hardt }, Title = { {S}ingularities in some geometric variational problems }, Booktitle = { {I}{C}{M} {B}erkeley }, Pages = { 540-550 }, Year = { 1986 } } @Incollection{ Har93, Author = { R. Hardt }, Title = { {S}ome new harmonic maps }, Booktitle = { {D}ifferential {G}eometry: partial differential equations on manifolds }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { American Math.\ Soc. }, Address = { Providence RI }, Volume = { 54:1 }, Pages = { 141-146 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ Har97, Author = { R.M. Hardt }, Title = { {S}ingularities of harmonic maps }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 34 }, Pages = { 15-34 }, Year = { 1997 } } @Incollection{ HarKin87, Author = { R. Hardt and D. Kinderlehrer }, Title = { {M}athematical questions of liquid crystal theory }, Booktitle = { {T}heory and applications of liquid crystals }, Editor = { J.L. Ericksen and D. Kinderlehrer }, Publisher = { Springer }, Address = { Berlin }, Volume = { 5 }, Series = { IMA Vol.\ Math.\ Appl. }, Year = { 1987 } } @Unpublished{ HarKinLin, Author = { R. Hardt and D. Kinderlehrer and F.H. Lin }, Title = { {E}nergy bounds for minimizing maps }, Note = { Preprint } } @Article{ HarKinLin86, Author = { R. Hardt and D. Kinderlehrer and F.H. Lin }, Title = { {E}xistence and partial regularity of static liquid crystal configurations }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 105 }, Pages = { 547-570 }, Year = { 1986 } } @Article{ HarLin, Author = { R. Hardt and F.H. Lin }, Title = { {S}ingularities for harmonic maps }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Note = { (to appear) } } @Article{ HarLin86, Author = { R. Hardt and F.H. Lin }, Title = { {A} remark on {${H}^1$}-mappings }, Journal = { Manuscripta Math. }, Volume = { 56 }, Pages = { 1-10 }, Year = { 1986 } } @Article{ HarLin87, Author = { R. Hardt and F.H. Lin }, Title = { {M}appings minimizing the {${L}^p$}-norm of the gradient }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 40 }, Pages = { 555-588 }, Year = { 1987 } } @Article{ HarLin89, Author = { R. Hardt and F.H. Lin }, Title = { {P}artially constrained boundary conditions with energy minimizing mappings }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 42 }, Pages = { 309-334 }, Year = { 1989 } } @Article{ HarLin89A, Author = { R. Hardt and F.H. Lin }, Title = { {S}tability of singularities of minimizing harmonic maps }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 113-123 }, Year = { 1989 } } @Article{ HarLin90, Author = { R. Hardt and F.H. Lin }, Title = { {T}he singular set of energy minimizing map from {${B}^4\rightarrow {S}^2$} }, Journal = { Manuscripta Math. }, Volume = { 69 }, Pages = { 275-289 }, Year = { 1990 } } @Article{ HarLin93, Author = { R. Hardt and F.H. Lin }, Title = { {H}armonic maps into round cones and singularities of nematic crystals }, Journal = { Math.\ Z. }, Volume = { 213 }, Pages = { 575-593 }, Year = { 1993 } } @Article{ HarLin95, Author = { R. Hardt and F.H. Lin }, Title = { {S}ingularities for {$p$}-energy minimizing unit vectorfields on planar domains }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 3 }, Pages = { 311-341 }, Year = { 1995 } } @Article{ HarLinPoo92, Author = { R. Hardt and F.H. Lin and C.C. Poon }, Title = { {A}xially symmetric harmonic maps minimizing a relaxed energy }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 45 }, Pages = { 417-459 }, Year = { 1992 } } @Article{ HarMou92, Author = { R. Hardt and L. Mou }, Title = { {H}armonic maps with fixed singular sets }, Journal = { J. Geom.\ Anal. }, Volume = { 2 }, Pages = { 445-488 }, Year = { 1992 } } @Article{ HarRos90, Author = { R. Hardt and H. Rosenberg }, Title = { {O}pen book structures and unicity of minimal submanifolds }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 40 }, Pages = { 701-708 }, Year = { 1990 } } @Article{ HarSim79, Author = { R. Hardt and L. Simon }, Title = { {B}oundary regularity and embedded minimal solutions for the oriented {P}lateau problem }, Journal = { Ann.\ of Math. }, Volume = { 110 }, Pages = { 439-486 }, Year = { 1979 } } @Article{ HarSim85, Author = { R. Hardt and L. Simon }, Title = { {A}rea minimizing hypersurfaces with isolated singularities }, Journal = { J. Reine Angew.\ Math. }, Volume = { 362 }, Pages = { 103-129 }, Year = { 1985 } } @Article{ HarSim89, Author = { R. Hardt and L. Simon }, Title = { {N}odal sets for solutions of elliptic equations }, Journal = { J. Differential Geom. }, Volume = { 30 }, Pages = { 505-522 }, Year = { 1989 } } @Article{ HarSaiShn84, Author = { J. Harnad and Y. Saint-Aubin and S. Shnider }, Title = { {B}\"acklund transformations for nonlinear sigma models with values in {R}iemannian symmetric spaces }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 92 }, Pages = { 329-367 }, Year = { 1984 } } @Book{ Har82, Author = { J. Harris }, Title = { {C}urves in projective space }, Publisher = { Presses Univ.\ Montr\'eal }, Year = { 1982 } } @Misc{ HarTuc, Author = { D. Hartley and R.W. Tucker }, Title = { {E}xtremal immersions and the extended frame bundles } } @Article{ Har67, Author = { P. Hartman }, Title = { {O}n homotopic harmonic maps }, Journal = { Canad.\ J. Math. }, Volume = { 19 }, Pages = { 673-687 }, Year = { 1967 } } @Article{ HarWin53, Author = { P. Hartman and A. Wintner }, Title = { {O}n the local behavior of solutions of nonparabolic partial differential equations }, Journal = { Amer.\ J. Math. }, Volume = { 75 }, Pages = { 449-476 }, Year = { 1953 } } @Article{ HarWin55, Author = { P. Hartman and A. Wintner }, Title = { {O}n the local behavior of solutions of nonparabolic partial differential equations, {I}{I}{I}. {A}pproximations by spherical harmonics }, Journal = { Amer.\ J. Math. }, Volume = { 77 }, Pages = { 453-474 }, Year = { 1955 } } @Article{ HarLaw74, Author = { R. Harvey and H.B. Lawson }, Title = { {B}oundaries of complex analytic varieties }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 80 }, Pages = { 180-183 }, Year = { 1974 } } @Article{ HarLaw75, Author = { R. Harvey and H.B. Lawson }, Title = { {O}n boundaries of complex analytic varieties, {I} }, Journal = { Ann.\ of Math. }, Volume = { 102 }, Pages = { 223-290 }, Year = { 1975 } } @Article{ HarLaw77, Author = { R. Harvey and H.B. Lawson }, Title = { {O}n boundaries of complex analytic varieties, {I}{I} }, Journal = { Ann.\ of Math. }, Volume = { 106 }, Pages = { 213-238 }, Year = { 1977 } } @Article{ HarLaw82, Author = { R. Harvey and H.B. Lawson }, Title = { {C}alibrated geometries }, Journal = { Acta Math. }, Volume = { 148 }, Pages = { 47-157 }, Year = { 1982 } } @Incollection{ HarLaw83, Author = { R. Harvey and H.B. Lawson }, Title = { {T}he minimal varieties associated to a closed form }, Booktitle = { {S}eminar on {M}inimal {S}urfaces }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 103 }, Pages = { 217-223 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Article{ Has81, Author = { T. Hasanis }, Title = { {C}haracterization of totally umbilic hypersurfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 81 }, Pages = { 447-450 }, Year = { 1981 } } @Article{ Has81A, Author = { T. Hasanis }, Title = { {M}inimal hypersurfaces of a manifold }, Journal = { Tensor (N.S.) }, Volume = { 35 }, Pages = { 262-266 }, Year = { 1981 } } @Article{ HasKou79, Author = { T. Hasanis and T. Koufogiorgos }, Title = { {A} characterization of a minimal hypersurface in {${\bf {R}}^{n+1}$} }, Journal = { Rev.\ Roumaine Math.\ Pures Appl. }, Volume = { 24 }, Pages = { 1213-1217 }, Year = { 1979 } } @Article{ HasKou84, Author = { T. Hasanis and D. Koutroufiotis }, Title = { {A} property of complete minimal surfaces }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 281 }, Pages = { 833-843 }, Year = { 1984 } } @Article{ Has80, Author = { T. Hasegawa }, Title = { {S}pectral geometry of closed minimal submanifolds in a space form, real and complex }, Journal = { Kodai Math.\ J. }, Volume = { 3 }, Pages = { 224-252 }, Year = { 1980 } } @Article{ Has97, Author = { H.S. Hashiguchi }, Title = { {T}he uniton numbers of the harmonic {$2$}-spheres in {${G}r_2({\bf {C}}^4)$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 49 }, Pages = { 81--105 }, Year = { 1997 } } @Misc{ Has, Author = { J. Hass }, Title = { {S}ingular curves and the {P}lateau problem } } @Unpublished{ Has81B, Author = { J. Hass }, Title = { {E}mbedded minimal surfaces in three and four dimensional manifolds }, Note = { Univ. California at Berkeley Thesis }, Year = { 1981 } } @Article{ Has84, Author = { J. Hass }, Title = { {C}omplete area minimizing surfaces which are not totally geodesic }, Journal = { Pacific J. Math. }, Volume = { 111 }, Pages = { 35-38 }, Year = { 1984 } } @Article{ Has84A, Author = { J. Hass }, Title = { {M}inimal surfaces in {S}iefert fibre spaces }, Journal = { Topology Appl. }, Volume = { 18 }, Pages = { 145-151 }, Year = { 1984 } } @Article{ Has86, Author = { J. Hass }, Title = { {M}inimal surfaces in foliated manifolds }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 61 }, Pages = { 1-32 }, Year = { 1986 } } @Article{ Has91, Author = { J. Hass }, Title = { {S}ingular curves and the {P}lateau problem }, Journal = { Internat.\ J. Math. }, Volume = { 2 }, Pages = { 1-16 }, Year = { 1991 } } @Incollection{ HasPitRub93, Author = { J. Hass and J.T. Pitts and J.H. Rubinstein }, Title = { {E}xistence of unstable minimal surfaces in manifolds with homology and applications to triply periodic minimal surfaces }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 147-162 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ HasSco88, Author = { J. Hass and P. Scott }, Title = { {T}he existence of least area surfaces in {$3$}-manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 310 }, Pages = { 87-114 }, Year = { 1988 } } @Article{ Hat87, Author = { K. Hatsuse }, Title = { {R}emarks on minimal immersions }, Journal = { Bull.\ Fac.\ Sci.\ Ibaraki Univ.\ Ser.\ A }, Volume = { 19 }, Pages = { 47-48 }, Year = { 1987 } } @Article{ Hef82, Author = { H. Hefter }, Title = { {D}ehnungsuntersuchungen an {S}ph\"arenabbildungen }, Journal = { Invent.\ Math. }, Volume = { 66 }, Pages = { 1-10 }, Year = { 1982 } } @Unpublished{ Hei95, Author = { M. Heil }, Title = { {N}umerical tools for the study of finite gap solutions of integrable systems }, Note = { TU-Berlin thesis }, Year = { 1995 } } @Article{ Hei58, Author = { H. Heilbronn }, Title = { {O}n the representation of homotopy classes of regular functions }, Journal = { Bull.\ Acad.\ Polon.\ Sci.\ S\'er.\ Sci.\ Tech. }, Volume = { 6 }, Pages = { 181-184 }, Year = { 1958 } } @Article{ HeiKilMar92, Author = { J. Heinonen and T. Kil{\"a}inen and O. Martio }, Title = { {H}armonic morphisms in non-linear potential theory }, Journal = { Nagoya Math.\ J. }, Volume = { 125 }, Pages = { 115-140 }, Year = { 1992 } } @Article{ Hei, Author = { E. Heinz }, Title = { {U}ber die {R}egularit\"at schwacher {L}\"osungen nonlinearer elliptischer {S}ysteme }, Journal = { Nachr.\ Akad.\ Wiss.\ G\"ottingen Math.-Phys.\ Kl.\ II }, Volume = { 1986 }, Pages = { 1-15 } } @Article{ Hei54, Author = { E. Heinz }, Title = { \"{U}ber die {E}xistenz einer {F}l\"ache konstanter mittlerer {K}r\"ummung bei vorgegebener {B}erandung }, Journal = { Math.\ Ann. }, Volume = { 127 }, Pages = { 258-287 }, Year = { 1954 } } @Article{ Hei65, Author = { E. Heinz }, Title = { {E}xistence theorems for one-to-one mappings associated with elliptic systems of second order, {I} }, Journal = { J. Analyse Math. }, Volume = { 15 }, Pages = { 325-352 }, Year = { 1965 } } @Article{ Hei66, Author = { E. Heinz }, Title = { {E}xistence theorems for one-to-one mappings associated with elliptic systems of second order, {I}{I} }, Journal = { J. Analyse Math. }, Volume = { 17 }, Pages = { 145-184 }, Year = { 1966 } } @Article{ Hei69, Author = { E. Heinz }, Title = { {O}n the nonexistence of a surface of constant mean curvature of finite area }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 35 }, Pages = { 249-252 }, Year = { 1969 } } @Article{ Hei75, Author = { E. Heinz }, Title = { {E}in regularit\"atssatz f\"ur schwache {L}\"osungen nonlinearer elliptische {S}ysteme }, Journal = { Nachr.\ Akad.\ Wiss.\ G\"ottingen Math.-Phys.\ Kl.\ II }, Volume = { 1 }, Pages = { 1-13 }, Year = { 1975 } } @Article{ HeiHil70, Author = { E. Heinz and S. Hildebrandt }, Title = { {T}he number of branch points of surfaces of bounded mean curvature }, Journal = { J. Differential Geom. }, Volume = { 4 }, Pages = { 227-235 }, Year = { 1970 } } @Article{ HeiHil70A, Author = { E. Heinz and S. Hildebrandt }, Title = { {S}ome remarks on minimal surfaces in {R}iemannian manifolds }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 23 }, Pages = { 371-377 }, Year = { 1970 } } @Article{ Hei55, Author = { H. Heinz }, Title = { {U}ber {F}l\"achen mit einendeutigen {P}rojection auf eine {E}bene deren {K}r\"ummung durch {U}ngleichungen eigeschr\"ankt sind }, Journal = { Math.\ Ann. }, Volume = { 129 }, Pages = { 451-454 }, Year = { 1955 } } @Article{ Hel66, Author = { S. Helgason }, Title = { {T}otally geodesic spheres in compact symmetric spaces }, Journal = { Math.\ Ann. }, Volume = { 165 }, Pages = { 309-317 }, Year = { 1966 } } @Article{ HenSch86, Author = { W. Hengartner and G. Schober }, Title = { {H}armonic mappings with given dilatation }, Journal = { J. London Math.\ Soc. }, Volume = { 33 }, Pages = { 473-483 }, Year = { 1986 } } @Article{ HenSch86A, Author = { W. Hengartner and G. Schober }, Title = { {O}n the boundary behavior of orientation preserving harmonic mappings }, Journal = { Complex Variables Theory Appl. }, Volume = { 5 }, Pages = { 197-208 }, Year = { 1986 } } @Incollection{ HenSch88, Author = { W. Hengartner and G. Schober }, Title = { {C}urvature estimates for some minimal surfaces }, Booktitle = { {C}omplex {A}nal. }, Address = { Basel }, Pages = { 87-100 }, Year = { 1988 } } @Misc{ HenSzn, Author = { W. Hengartner and J. Sznal }, Title = { {U}nivalent harmonic ring mappings vanishing on the interior boundary } } @Unpublished{ Hen/3, Author = { P. Hennebert }, Title = { {M}inimisation de l'\'energie en th\'eorie math\'ematique des cristaux liquides }, Note = { Univ. Libre Bruxelles. M\'emoire }, Year = { 1992/3 } } @Misc{ Her, Author = { P. Hermann }, Title = { {E}in {B}eweis des {S}atzes von {R}uh-{V}ilms } } @Article{ Her60, Author = { R. Hermann }, Title = { {E}xistence in the large of totally geodesic submanifolds of {R}iemannian spaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 66 }, Pages = { 59-61 }, Year = { 1960 } } @Article{ Her60A, Author = { R. Hermann }, Title = { {O}n geodesics that are also orbits }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 66 }, Pages = { 91-93 }, Year = { 1960 } } @Article{ Her60B, Author = { R. Hermann }, Title = { {A} sufficient condition that a map of {R}iemannian manifolds be a fibre bundle }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 11 }, Pages = { 236-242 }, Year = { 1960 } } @Article{ Her70, Author = { R. Hermann }, Title = { {C}urrent algebras, the {S}ugawara model, and differential geometry }, Journal = { J. Math.\ Phys. }, Volume = { 11 }, Pages = { 1825-1829 }, Year = { 1970 } } @Misc{ HerA, Author = { L. Hern{\'a}ndez }, Title = { {K}\"ahler manifolds and {$1/4$}-pinching } } @Article{ Her70A, Author = { J. Hersch }, Title = { {Q}uatre propri\'et\'es isop\'erim\'etriques de membranes sph\'eriques homog\`enes }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 270 }, Pages = { 1645-1648 }, Year = { 1970 } } @Article{ Her62, Author = { R.M. Herv{\'e} }, Title = { {R}echerches axiomatiques sur la th{\'e}orie des fonctions surharmoniques et du potentiel }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 12 }, Pages = { 415-571 }, Year = { 1962 } } @Article{ HesSchUhl80, Author = { H. Hess and R. Schrader and D.A. Uhlenbrock }, Title = { {K}ato's inequality and the spectral distribution of {L}aplacians on compact {R}iemannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 15 }, Pages = { 27-37 }, Year = { 1980 } } @Article{ Hig93, Author = { M. Higaki }, Title = { {T}he nullity of harmonic tori into {L}ie groups }, Journal = { J. Fac.\ Sci.\ Univ.\ Tokyo Sect.\ IA Math. }, Volume = { 40 }, Pages = { 203-228 }, Year = { 1993 } } @Article{ Hil69, Author = { S. Hildebrandt }, Title = { {B}oundary behavior of minimal surfaces }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 35 }, Pages = { 47-82 }, Year = { 1969 } } @Article{ Hil69A, Author = { S. Hildebrandt }, Title = { \"{U}ber {F}l\"achen konstanter mittlerer {K}r\"ummung }, Journal = { Math.\ Z. }, Volume = { 112 }, Pages = { 107-144 }, Year = { 1969 } } @Article{ Hil70, Author = { S. Hildebrandt }, Title = { {O}n the {P}lateau problem for surfaces of constant mean curvature }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 23 }, Pages = { 97-114 }, Year = { 1970 } } @Article{ Hil72, Author = { S. Hildebrandt }, Title = { {M}aximum principles for minimal surfaces and for surfaces of constant mean curvature }, Journal = { Math.\ Z. }, Volume = { 128 }, Pages = { 253-269 }, Year = { 1972 } } @Incollection{ Hil81, Author = { S. Hildebrandt }, Title = { {B}oundary behavior of minimal surfaces with free boundaries }, Booktitle = { {R}ecent contributions to nonlinear partial differential equations }, Editor = { H. Berestycki and H. Brezis }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 50 }, Pages = { 77-102 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1981 } } @Incollection{ Hil82, Author = { S. Hildebrandt }, Title = { {N}onlinear elliptic systems and harmonic mappings }, Booktitle = { {P}roc. 1980 {B}eijing {S}ymp. on {D}iff. {G}eom. and {D}iff. {E}quations }, Editor = { S.S. Chern and W.J. Wu }, Publisher = { Gordon and Breach }, Address = { New York }, Pages = { 481-615 }, Year = { 1982 } } @Unpublished{ Hil83, Author = { S. Hildebrandt }, Title = { {E}uler und die {V}ariationsrechnung }, Note = { Bonn preprint }, Year = { 1983 } } @Incollection{ Hil83A, Author = { S. Hildebrandt }, Title = { {L}iouville theorems for harmonic mappings, and an approach to {B}ernstein theorems }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 107-131 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Unpublished{ Hil83B, Author = { S. Hildebrandt }, Title = { {P}artielle {D}ifferentialgleichungen und {D}ifferentialgeometrie }, Note = { SFB 72 Bonn preprint }, Year = { 1983 } } @Incollection{ Hil83C, Author = { S. Hildebrandt }, Title = { {Q}uasilinear elliptic systems in diagonal form }, Booktitle = { {S}yst. {N}onlinear {P}.{E}.{D}. }, Editor = { J.M. Ball }, Publisher = { Reidel }, Address = { Dortrecht, Boston, London }, Pages = { 173-217 }, Year = { 1983 } } @Incollection{ Hil83D, Author = { S. Hildebrandt }, Title = { {V}ariationsrechnung -- ein dreihundertj\"ahriges mathematisches {F}orschungsgebiet }, Booktitle = { {F}orsch. {B}und. {D}eutschland }, Pages = { 481-488 }, Year = { 1983 } } @Incollection{ Hil85, Author = { S. Hildebrandt }, Title = { {H}armonic mappings of {R}iemannian manifolds }, Booktitle = { {H}armonic {M}appings and {M}inimal {I}mmersions, {M}ontecatini 1984 }, Editor = { E. Giusti }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1161 }, Pages = { 1-117 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Article{ HilJosWid80, Author = { S. Hildebrandt and J. Jost and K.O. Widman }, Title = { {H}armonic mappings and minimal submanifolds }, Journal = { Invent.\ Math. }, Volume = { 62 }, Pages = { 269-298 }, Year = { 1980 } } @Article{ HilJag70, Author = { S. Hildebrandt and W. J{\"a}ger }, Title = { {O}n the regularity of surfaces with prescribed mean curvature at a free boundary }, Journal = { Math.\ Z. }, Volume = { 118 }, Pages = { 289-308 }, Year = { 1970 } } @Article{ HilKau72, Author = { S. Hildebrandt and H. Kaul }, Title = { {T}wo-dimensional variational problems... }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 25 }, Pages = { 187-223 }, Year = { 1972 } } @Article{ HilKauWid75, Author = { S. Hildebrandt and H. Kaul and K.O. Widman }, Title = { {H}armonic mappings into {R}iemannian manifolds with non-positive sectional curvature }, Journal = { Math.\ Scand. }, Volume = { 37 }, Pages = { 257-263 }, Year = { 1975 } } @Article{ HilKauWid76, Author = { S. Hildebrandt and H. Kaul and K.O. Widman }, Title = { {D}irichlet's boundary value problem for harmonic mappings of {R}iemannian manifolds }, Journal = { Math.\ Z. }, Volume = { 147 }, Pages = { 225-236 }, Year = { 1976 } } @Article{ HilKauWid77, Author = { S. Hildebrandt and H. Kaul and K.O. Widman }, Title = { {A}n existence theorem for harmonic maps of {R}iemannian manifolds }, Journal = { Acta Math. }, Volume = { 138 }, Pages = { 1-16 }, Year = { 1977 } } @Article{ HilNit79, Author = { S. Hildebrandt and J.C.C. Nitsche }, Title = { {M}inimal surfaces with free boundaries }, Journal = { Acta Math. }, Volume = { 143 }, Pages = { 251-272 }, Year = { 1979 } } @Article{ HilNit82, Author = { S. Hildebrandt and J.C.C. Nitsche }, Title = { {A} uniqueness theorem for surfaces of least area with partially free boundaries on obstacles }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 79 }, Pages = { 189-218 }, Year = { 1982 } } @Article{ HilSau91, Author = { S. Hildebrandt and F. Sauvigny }, Title = { {E}mbeddedness and uniqueness of minimal surfaces solving a partially free boundary problem }, Journal = { J. Reine Angew.\ Math. }, Volume = { 422 }, Pages = { 69-89 }, Year = { 1991 } } @Article{ HilSau92, Author = { S. Hildebrandt and F. Sauvigny }, Title = { {O}n one-to-one harmonic mappings and minimal surfaces }, Journal = { Nachr.\ Akad.\ Wiss.\ G\"ottingen Math.-Phys.\ Kl.\ II }, Volume = { 3 }, Pages = { 73-93 }, Year = { 1992 } } @Misc{ HilTro87, Author = { S. Hildebrandt and A.J. Tromba }, Title = { {P}anoptimum }, Address = { Heidelberg }, Year = { 1987 } } @Article{ HilWid75, Author = { S. Hildebrandt and K.-O. Widman }, Title = { {S}ome regularity results for quasilinear elliptic systems of second order }, Journal = { Math.\ Z. }, Volume = { 142 }, Pages = { 67-86 }, Year = { 1975 } } @Article{ HirSch88, Author = { T. Hirschmann and R. Schimming }, Title = { {H}armonic maps from spacetime and their coupling to gravitation }, Journal = { Astronom.\ Nachr. }, Volume = { 309 }, Pages = { 311-321 }, Year = { 1988 } } @Article{ Hit82, Author = { N.J. Hitchin }, Title = { {M}onopoles and geodesics }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 83 }, Pages = { 579-602 }, Year = { 1982 } } @Book{ Hit87, Author = { N.J. Hitchin }, Title = { {M}onopoles, minimal surfaces and algebraic curves }, Publisher = { Presses Univ.\ Montr\'eal }, Address = { Montr\'eal }, Volume = { 105 }, Series = { S\'em.\ Math.\ Sup. }, Year = { 1987 } } @Article{ Hit87A, Author = { N.J. Hitchin }, Title = { {T}he self-duality equations on a {R}iemann surface }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 55 }, Pages = { 59-126 }, Year = { 1987 } } @Incollection{ Hit88, Author = { N.J. Hitchin }, Title = { {H}armonic maps from {${T}^2$} to {${S}^3$} }, Booktitle = { {H}armonic mappings, twistors, and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 103-112 }, Year = { 1988 } } @Article{ Hit90, Author = { N.J. Hitchin }, Title = { {H}armonic maps from a {$2$}-torus to the {$3$}-sphere }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 627-710 }, Year = { 1990 } } @Article{ Hit92, Author = { N.J. Hitchin }, Title = { {L}ie groups and {T}eichm\"uller space }, Journal = { Topology }, Volume = { 31 }, Pages = { 449-473 }, Year = { 1992 } } @Unpublished{ Hit96, Author = { N.J. Hitchin }, Title = { {I}ntegrable systems in {R}iemannian geometry }, Note = { Preprint }, Year = { 1996 } } @Misc{ Hof, Author = { D.A. Hoffman }, Title = { {N}ew examples of singly-periodic minimal surfaces and their qualitative behaviour } } @Article{ Hof73, Author = { D.A. Hoffman }, Title = { {S}urfaces of constant mean curvature in manifolds of constant curvature }, Journal = { J. Differential Geom. }, Volume = { 8 }, Pages = { 161-176 }, Year = { 1973 } } @Article{ Hof82, Author = { D.A. Hoffman }, Title = { {W}hen is a map a {G}auss map? }, Journal = { I.M.P.A. }, Pages = { 27-38 }, Year = { 1982 } } @Incollection{ Hof85, Author = { D.A. Hoffman }, Title = { {E}mbedded minimal surfaces, computer graphics and elliptic functions }, Booktitle = { {G}lobal differential geometry and global analysis 1984 }, Editor = { D. Ferus and R.B. Gardner and S. Helgason and U. Simon }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1156 }, Pages = { 204-215 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Article{ Hof90, Author = { D.A. Hoffman }, Title = { {S}ome basic facts, old and new, about triply periodic embedded minimal surfaces }, Journal = { Colloque de Physique C7 Suppl.\ 23 }, Volume = { 51 }, Pages = { 197-208 }, Year = { 1990 } } @Misc{ HofKarRos, Author = { D.A. Hoffman and H. Karcher and H. Rosenberg }, Title = { {E}mbedded minimal annuli in {${\bf {R}}^3$} bounded by a pair of straight lines } } @Article{ HofKarWei93, Author = { D.A. Hoffman and H. Karcher and F.S. Wei }, Title = { {A}dding handles to the helicoid }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 29 }, Pages = { 77-84 }, Year = { 1993 } } @Incollection{ HofKarWei93A, Author = { D.A. Hoffman and H. Karcher and F.S. Wei }, Title = { {T}he genus one helicoid and the minimal surfaces that led to its discovery }, Booktitle = { {G}lobal analysis in modern mathematics }, Publisher = { Publish or Perish }, Address = { Houston TX }, Pages = { 119-170 }, Year = { 1993 } } @Misc{ HofMee, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {M}inimal surfaces based on the catenoid } } @Misc{ HofMeeA, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {O}ne parameter families of embedded complete minimal surfaces of finite topology } } @Article{ HofMee85, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {A} complete embedded minimal surface in {${\bf {R}}^3$} with genus one and three ends }, Journal = { J. Differential Geom. }, Volume = { 21 }, Pages = { 109-127 }, Year = { 1985 } } @Article{ HofMee85A, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {C}omplete embedded minimal surfaces of finite total curvature }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 12 }, Pages = { 134-136 }, Year = { 1985 } } @Article{ HofMee87, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {P}roperties of properly embedded minimal surfaces of finite topology }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 17 }, Pages = { 296-300 }, Year = { 1987 } } @Article{ HofMee88, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {A} variational approach to the existence of complete embedded minimal surfaces }, Journal = { Duke Math.\ J. }, Volume = { 57 }, Pages = { 877-893 }, Year = { 1988 } } @Article{ HofMee89, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {T}he asymptotic behavior of properly embedded minimal surfaces of finite topology }, Journal = { J. Amer.\ Math.\ Soc. }, Volume = { 2 }, Pages = { 667-682 }, Year = { 1989 } } @Article{ HofMee90, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {E}mbedded minimal surfaces of finite topology }, Journal = { Ann.\ of Math. }, Volume = { 131 }, Pages = { 1-34 }, Year = { 1990 } } @Article{ HofMee90A, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {L}imits of minimal surfaces and {S}cherk's second surface }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 111 }, Pages = { 181-195 }, Year = { 1990 } } @Article{ HofMee90B, Author = { D.A. Hoffman and W.H. Meeks }, Title = { {T}he strong halfspace theorem for minimal surfaces }, Journal = { Invent.\ Math. }, Volume = { 101 }, Pages = { 373-377 }, Year = { 1990 } } @Book{ HofOss80, Author = { D.A. Hoffman and R. Osserman }, Title = { {T}he geometry of the generalized {G}auss map }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 236 }, Series = { Mem.\ Amer.\ Math.\ Soc. }, Year = { 1980 } } @Article{ HofOss82, Author = { D.A. Hoffman and R. Osserman }, Title = { {T}he area of the generalized {G}aussian image and the stability of minimal surfaces in {${S}^n$} and {${\bf {R}}^n$} }, Journal = { Math.\ Ann. }, Volume = { 260 }, Pages = { 437-452 }, Year = { 1982 } } @Article{ HofOss83, Author = { D.A. Hoffman and R. Osserman }, Title = { {T}he {G}auss map of surfaces in {${\bf {R}}^n$} }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 733-754 }, Year = { 1983 } } @Article{ HofOss85, Author = { D.A. Hoffman and R. Osserman }, Title = { {T}he {G}auss map of surfaces in {${\bf {R}}^3$} and {${\bf {R}}^4$} }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 50 }, Pages = { 27-56 }, Year = { 1985 } } @Article{ HofOss90, Author = { D.A. Hoffman and R. Osserman }, Title = { {M}inimal surfaces based on the catenoid }, Journal = { Amer.\ Math.\ Monthly }, Volume = { 97 }, Pages = { 702-730 }, Year = { 1990 } } @Article{ HofOssSch82, Author = { D.A. Hoffman and R. Osserman and R. Schoen }, Title = { {O}n the {G}auss map of surfaces of constant mean curvature in {${\bf {R}}^3$} and {${\bf {R}}^4$} }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 57 }, Pages = { 519-531 }, Year = { 1982 } } @Unpublished{ Hoh94, Author = { J. Hohrein }, Title = { {E}xistence of unstable minimal surfaces of higher genus in manifolds of nonpositive curvature }, Address = { Heidelberg }, Note = { Thesis }, Year = { 1994 } } @Article{ HonYan93, Author = { J.Q. Hong and Y.H. Yang }, Title = { {S}ome results on exponentially harmonic maps }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 14 }, Pages = { 686-691 }, Note = { (Chinese) }, Year = { 1993 } } @Article{ Hon89, Author = { J.X. Hong }, Title = { {H}armonic maps defined on a manfold with a degenerate metric }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 106 }, Pages = { 471-479 }, Year = { 1989 } } @Article{ HonLin90, Author = { J.X. Hong and J.Q. Lin }, Title = { {O}n existence and nonexistence of some harmonic maps }, Journal = { Acta Math.\ Sinica }, Volume = { 6 }, Pages = { 1-9 }, Year = { 1990 } } @Misc{ Hon, Author = { M.C. Hong }, Title = { {T}he equator map and the negative exponential function } } @Article{ Hon92, Author = { M.C. Hong }, Title = { {L}iouville theorems for exponentially harmonic functions on {R}iemannian manifolds }, Journal = { Manuscripta Math. }, Volume = { 77 }, Pages = { 41-46 }, Year = { 1992 } } @Article{ Hon92A, Author = { M.C. Hong }, Title = { {O}n the conformal equivalence of harmonic maps and exponentially harmonic maps }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 24 }, Pages = { 488-492 }, Year = { 1992 } } @Article{ HonLem95, Author = { M.C. Hong and L. Lemaire }, Title = { {M}ultiple solutions of the static {L}andau-{L}ipschitz equation from {${B}^2$} into {${S}^2$} }, Journal = { Math.\ Z. }, Volume = { 220 }, Pages = { 295-306 }, Year = { 1995 } } @Article{ Hop51, Author = { H. Hopf }, Title = { \"{U}ber {F}l\"achen mit einer {R}elation zwischen den {H}auptkr\"ummungen }, Journal = { Math.\ Nachr. }, Volume = { 4 }, Pages = { 232-249 }, Year = { 1950/51 } } @Article{ HopNic87, Author = { J. Hoppe and H. Nicolai }, Title = { {R}elativistic minimal surfaces }, Journal = { Phys.\ Lett.\ B }, Volume = { 196 }, Pages = { 451-455 }, Year = { 1987 } } @Misc{ HorKik, Author = { H. Horihata and K. Kikuchi }, Title = { {A} construction of solutions satisfying a {C}acciopoli inequality for nonlinear parabolic equations associated to a variational functional of harmonic type } } @Article{ Hor, Author = { R. Horiuchi }, Title = { {O}n the existence of meromorphic functions with certain lower order on non-hyperelliptic {R}iemann surfaces }, Journal = { J. Math.\ Kyoto Univ. } } @Article{ Hor93, Author = { T. Horsin-Molinaro }, Title = { {L}ong-time existence for a solution of the equation of evolution of harmonic maps into an ellipsoid }, Journal = { Manuscripta Math. }, Volume = { 78 }, Pages = { 317-339 }, Year = { 1993 } } @Article{ Hou92, Author = { Z.X. Hou }, Title = { {O}n harmonic maps between generalized flag manifolds }, Journal = { Acta Math.\ Sinica }, Volume = { 8 }, Pages = { 1-16 }, Year = { 1992 } } @Article{ HowSmy71, Author = { A. Howard and B. Smyth }, Title = { {K}\"ahler surfaces of nonnegative curvature }, Journal = { J. Differential Geom. }, Volume = { 5 }, Pages = { 491-502 }, Year = { 1971 } } @Article{ HowSmyWu81, Author = { A. Howard and B. Smyth and H.H. Wu }, Title = { {O}n compact {K}\"ahler manifolds of nonnegative bisectional curvature {I} }, Journal = { Acta Math. }, Volume = { 147 }, Pages = { 51-56 }, Year = { 1981 } } @Article{ How85, Author = { R. Howard }, Title = { {T}he non-existence of stable submanifolds, varifolds and harmonic maps in sufficiently pinched simply connected {R}iemannian manifolds }, Journal = { Michigan Math.\ J. }, Volume = { 32 }, Pages = { 321-334 }, Year = { 1985 } } @Article{ HowWei86, Author = { R. Howard and S.W. Wei }, Title = { {N}on-existence of stable harmonic maps to and from certain homogeneous spaces and submanifolds of {E}uclidean space }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 294 }, Pages = { 319-331 }, Year = { 1986 } } @Article{ HowPap88, Author = { P.S. Howe and G. Papadopoulos }, Title = { {F}urther remarks on the geometry of two-dimensional non-linear {$\sigma$} models }, Journal = { Classical Quantum Gravity }, Volume = { 5 }, Pages = { 1647-1661 }, Year = { 1988 } } @Article{ HsiHsi80, Author = { W.T. Hsiang and W.Y. Hsiang }, Title = { {E}xamples of codimension-one closed minimal submanifold in some symmetric spaces {I} }, Journal = { J. Differential Geom. }, Volume = { 15 }, Pages = { 543-551 }, Year = { 1980 } } @Article{ HsiHsi82, Author = { W.T. Hsiang and W.Y. Hsiang }, Title = { {O}n the existence of codimension-one minimal spheres in compact symmetric spaces of rank {$2$}. {I}{I} }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 583-594 }, Year = { 1982 } } @Article{ HsiHsi85, Author = { W.T. Hsiang and W.Y. Hsiang }, Title = { {O}n the construction of constant mean curvature imbeddings of exotic and/or knotted spheres into {${S}^n(1)$} }, Journal = { Invent.\ Math. }, Volume = { 82 }, Pages = { 423-445 }, Year = { 1985 } } @Article{ HsiHsi87, Author = { W.T. Hsiang and W.Y. Hsiang }, Title = { {O}n the construction of codimension two minimal immersions of exotic spheres into {E}uclidean spheres {I}{I} }, Journal = { Math.\ Z. }, Volume = { 195 }, Pages = { 301-313 }, Year = { 1987 } } @Article{ HsiHsiSte85, Author = { W.T. Hsiang and W.Y. Hsiang and I. Sterling }, Title = { {O}n the construction of codimension two minimal immersions of exotic spheres into {E}uclidean spheres }, Journal = { Invent.\ Math. }, Volume = { 82 }, Pages = { 447-460 }, Year = { 1985 } } @Article{ HsiHsiTom83, Author = { W.T. Hsiang and W.Y. Hsiang and P. Tomter }, Title = { {O}n the construction of infinitely many mutually noncongruent examples of minimal embeddings of {${S}^{2n-1}$} into {${C}{P}^n$}, {$n\geq 2$} }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 8 }, Pages = { 463-465 }, Year = { 1983 } } @Article{ HsiHsiTom88, Author = { W.T. Hsiang and W.Y. Hsiang and P. Tomter }, Title = { {O}n the existence of minimal hyperspheres in compact symmetric spaces }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 21 }, Pages = { 287-305 }, Year = { 1988 } } @Article{ HsiTenYu83, Author = { W.T. Hsiang and Z.H. Teng and W.C. Yu }, Title = { {N}ew examples of constant mean curvature immersions of {$(2k-1)$}-spheres into {E}uclidean {$2k$}-space }, Journal = { Ann.\ of Math. }, Volume = { 117 }, Pages = { 609-625 }, Year = { 1983 } } @Article{ Hsi, Author = { W.Y. Hsiang }, Title = { {O}n the construction of infinitely many congruence classes of imbedded closed minimal hypersurfaces in {${S}^n(1)$} for all {$n\geq 3$} }, Journal = { Duke Math.\ J. }, Volume = { 55 }, Pages = { 361-367 } } @Article{ Hsi66, Author = { W.Y. Hsiang }, Title = { {O}n the compact homogeneous minimal submanifolds }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 56 }, Pages = { 5-6 }, Year = { 1966 } } @Article{ Hsi67, Author = { W.Y. Hsiang }, Title = { {R}emarks on closed minimal submanifolds in the standard {R}iemannian {$m$}-sphere }, Journal = { J. Differential Geom. }, Volume = { 1 }, Pages = { 257-267 }, Year = { 1967 } } @Article{ Hsi82, Author = { W.Y. Hsiang }, Title = { {G}eneralized rotational hypersurfaces of constant mean curvature in the euclidean spheres, {I} }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 337-356 }, Year = { 1982 } } @Article{ Hsi82A, Author = { W.Y. Hsiang }, Title = { {O}n generalizations of theorems of {A}.{D}. {A}lexandrov and {C}. {D}elaunay on hypersurfaces of constant mean curvature }, Journal = { Duke Math.\ J. }, Volume = { 49 }, Pages = { 485-496 }, Year = { 1982 } } @Article{ Hsi83, Author = { W.Y. Hsiang }, Title = { {M}inimal cones and the spherical {B}ernstein problem. {I} }, Journal = { Ann.\ of Math. }, Volume = { 118 }, Pages = { 61-73 }, Year = { 1983 } } @Article{ Hsi83A, Author = { W.Y. Hsiang }, Title = { {M}inimal cones and the spherical {B}ernstein problem. {I}{I} }, Journal = { Invent.\ Math. }, Volume = { 74 }, Pages = { 351-369 }, Year = { 1983 } } @Article{ Hsi92, Author = { W.Y. Hsiang }, Title = { {O}n soap bubbles and isoperimetric regions in noncompact symmetric spaces {I} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 44 }, Pages = { 151-175 }, Year = { 1992 } } @Incollection{ Hsi93, Author = { W.Y. Hsiang }, Title = { {C}losed minimal surfaces in the spheres }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 163-173 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Misc{ HsiHuy, Author = { W.Y. Hsiang and H.L. Huynh }, Title = { {O}n spherical soap bubbles in non-compact symmetric spaces of rank {$\leq 2$} } } @Article{ HsiHuy87, Author = { W.Y. Hsiang and H.L. Huynh }, Title = { {G}eneralized rotational hypersurfaces of constant mean curvature in the {E}uclidean spaces {I}{I} }, Journal = { Pacific J. Math. }, Volume = { 130 }, Pages = { 75-95 }, Year = { 1987 } } @Article{ HsiLaw71, Author = { W.Y. Hsiang and H.B. Lawson }, Title = { {M}inimal submanifolds of low cohomogeneity }, Journal = { J. Differential Geom. }, Volume = { 5 }, Pages = { 1-38 }, Year = { 1971 } } @Unpublished{ HsiPalTer, Author = { W.Y. Hsiang and R.S. Palais and C.L. Terng }, Title = { {T}opology of isoparametric submanifolds of {E}uclidean space }, Note = { preprint } } @Article{ HsiPalTer88, Author = { W.Y. Hsiang and R.S. Palais and C.L. Terng }, Title = { {T}he topology of isoparametric submanifolds }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 423-460 }, Year = { 1988 } } @Article{ HsiSte84, Author = { W.Y. Hsiang and I. Sterling }, Title = { {O}n the construction of non-equatorial minimal hyperspheres in {${S}^n (1)$} with stable cones in {${\bf {R}}^{n+1}$} }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 81 }, Pages = { 8035-8036 }, Year = { 1984 } } @Article{ HsiSte86, Author = { W.Y. Hsiang and I. Sterling }, Title = { {M}inimal cones and the spherical {B}ernstein problem {I}{I}{I} }, Journal = { Invent.\ Math. }, Volume = { 85 }, Pages = { 223-247 }, Year = { 1986 } } @Article{ HsiTenYu82, Author = { W.Y. Hsiang and Z.H. Teng and W. Yu }, Title = { {E}xamples of constant mean curvature immersions of {$3$}-sphere into euclidean {$4$}-space }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 79 }, Pages = { 3931-3932 }, Year = { 1982 } } @Article{ HsiTenYu83A, Author = { W.Y. Hsiang and Z.H. Teng and W.C. Yu }, Title = { {N}ew examples of constant mean curvature immersions of {$(2k-1)$}-spheres into {E}uclidean {$2k$}-space }, Journal = { Ann.\ of Math. }, Volume = { 117 }, Pages = { 609-625 }, Year = { 1983 } } @Misc{ HsiTom, Author = { W.Y. Hsiang and P. Tomter }, Title = { {M}inimal immersions of spheres and the {A}lmgren--{C}alabi theorem } } @Article{ HsiTom87, Author = { W.Y. Hsiang and P. Tomter }, Title = { {O}n minimal immersions of {${S}^{n-1}$} in {${S}^n(1)$}, {$n\geq 4$} }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 20 }, Pages = { 201-214 }, Year = { 1987 } } @Article{ HsiYu81, Author = { W.Y. Hsiang and W. Yu }, Title = { {A} generalization of a theorem of {D}elaunay }, Journal = { J. Differential Geom. }, Volume = { 16 }, Pages = { 161-177 }, Year = { 1981 } } @Article{ HsiWan94, Author = { C.C. Hsieh and A.N. Wang }, Title = { {M}inimal tori in {${S}^2\times {S}^3$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 122 }, Pages = { 323-324 }, Year = { 1994 } } @Article{ HsiMug77, Author = { C.C. Hsiung and L.R. Mugridge }, Title = { {C}onformal invariants of submanifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 62 }, Pages = { 316-318 }, Year = { 1977 } } @Article{ Hsu72, Author = { A.C.L. Hsu }, Title = { {A} characterization of the {H}opf map by stretch }, Journal = { Math.\ Z. }, Volume = { 129 }, Pages = { 195-206 }, Year = { 1972 } } @Article{ Hsu72A, Author = { A.C.L. Hsu }, Title = { {S}tretch and degree }, Journal = { Tamkang J. Math. }, Volume = { 31 }, Pages = { 181-190 }, Year = { 1972 } } @Article{ HsuMar85, Author = { P. Hsu and P. March }, Title = { {T}he limiting angle of certain {R}iemannian {B}rownian motions }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 38 }, Pages = { 755-768 }, Year = { 1985 } } @Article{ Hsu91, Author = { Y.J. Hsu }, Title = { {A} global pinching theorem for compact minimal surfaces in {${S}^3$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 113 }, Pages = { 1041-1044 }, Year = { 1991 } } @Incollection{ Hu, Author = { H.S. Hu }, Title = { {T}he geometry of the sine-{L}aplace and sinh {L}aplace equation }, Booktitle = { {P}roc. {T}hird {G}rossmann {S}ymposium } } @Article{ Hu82, Author = { H.S. Hu }, Title = { {S}ine-{L}aplace equation and sinh-{L}aplace equation and harmonic maps }, Journal = { Manuscripta Math. }, Volume = { 40 }, Pages = { 205-216 }, Year = { 1982 } } @Article{ Hu84, Author = { H.S. Hu }, Title = { {A} nonexistence theorem for harmonic maps with slowly divergent energy }, Journal = { Chinese Ann.\ Math. }, Volume = { 5 }, Pages = { 737-740 }, Year = { 1984 } } @Incollection{ Hu84A, Author = { H.S. Hu }, Title = { {S}ome nonexistence theorems for massive {Y}ang--{M}ills fields and harmonic maps }, Booktitle = { {G}ravitational {G}eometry and {R}elativistic {P}hysics, {A}ussois 1984 }, Publisher = { Springer }, Address = { Berlin }, Volume = { 212 }, Pages = { 107-116 }, Series = { Lecture Notes in Phys. }, Year = { 1984 } } @Article{ Hu85, Author = { H.S. Hu }, Title = { {T}he construction of hyperbolic surfaces in {$3$}-dimensional {M}inkowski space and sinh-{L}aplace equation }, Journal = { Acta Math.\ Sinica }, Volume = { 1 }, Pages = { 79-86 }, Year = { 1985 } } @Incollection{ Hu85A, Author = { H.S. Hu }, Title = { {S}ome nonlinear {P}{D}{E}s and harmonic maps }, Booktitle = { {S}ympl. geo. and mechanics }, Publisher = { Hermann }, Address = { Paris }, Pages = { 76-85 }, Series = { Travaux en Cours }, Year = { 1985 } } @Article{ Hu87, Author = { H.S. Hu }, Title = { {N}onexistence theorems for {Y}ang--{M}ills fields and harmonic maps in the {S}chwarschild space-time {I} }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 14 }, Pages = { 253-262 }, Year = { 1987 } } @Article{ HuPan86, Author = { H.S. Hu and Y.L. Pan }, Title = { {A} theorem of {L}iouville's type on harmonic maps with finite or slowly diverging energy }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 7 }, Pages = { 345-349 }, Year = { 1986 } } @Article{ HuPanShe87, Author = { H.S. Hu and Y.L. Pan and Y.B. Shen }, Title = { {H}armonic maps and a pinching theorem for positively curved hypersurfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 99 }, Pages = { 182-186 }, Year = { 1987 } } @Article{ HuWu87, Author = { H.S. Hu and S.Y. Wu }, Title = { {N}onexistence theorems for {Y}ang--{M}ills fields and harmonic maps in the {S}chwarschild space-time {I}{I} }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 14 }, Pages = { 343-351 }, Year = { 1987 } } @Misc{ Hua, Author = { H. Huang }, Title = { {$\{G}amma$}-martingale and harmonic maps } } @Article{ HuaKen91, Author = { H. Huang and W.S. Kendall }, Title = { {C}orrection note to ``{M}artingales on manifolds and harmonic maps'' }, Journal = { Stochastics }, Volume = { 37 }, Pages = { 253-257 }, Year = { 1991 } } @Article{ Hua91, Author = { X.G. Huang }, Title = { {C}losed surfaces with prescribed mean curvature in {${\bf {R}}^3$} }, Journal = { Sci.\ China Ser.\ A }, Volume = { 34 }, Pages = { 1162-1173 }, Year = { 1991 } } @Article{ Hua93, Author = { X.G. Huang }, Title = { {A} maximum principle on complete {R}iemannian manifolds }, Journal = { Chinese Ann.\ Math. }, Volume = { 14 }, Pages = { 175-186 }, Year = { 1993 } } @Misc{ HugSha, Author = { L.P. Hughston and W.T. Shaw }, Title = { {C}lassical strings in {$10$} dimensions } } @Misc{ HugShaA, Author = { L.P. Hughston and W.T. Shaw }, Title = { {R}eal strings in {$4$} dimensions } } @Article{ HugSha87, Author = { L.P. Hughston and W.T. Shaw }, Title = { {M}inimal curves in six dimensions }, Journal = { Classical Quantum Gravity }, Volume = { 4 }, Pages = { 869-892 }, Year = { 1987 } } @Article{ Hui84, Author = { G. Huisken }, Title = { {F}low by mean curvature of convex surfaces into spheres }, Journal = { J. Differential Geom. }, Volume = { 20 }, Pages = { 237-266 }, Year = { 1984 } } @Article{ Hui90, Author = { G. Huisken }, Title = { {A}symptotic behaviour for singularities of the mean curvature flow }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 285-299 }, Year = { 1990 } } @Incollection{ Hui93, Author = { G. Huisken }, Title = { {L}ocal and global behaviour of hypersurfaces moving by mean curvature }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 175-191 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Misc{ Hun, Author = { N. Hungerb{\"u}hler }, Title = { {T}he weak solutions to the evolution problem of {$p$}-harmonic maps into spheres } } @Article{ HunSax91, Author = { J.K. Hunter and R. Saxton }, Title = { {D}ynamics of director fields }, Journal = { SIAM J. Appl.\ Math. }, Volume = { 51 }, Pages = { 1498-1521 }, Year = { 1991 } } @Article{ Hur96, Author = { J.C. Hurtubise }, Title = { {H}olomorphic maps of a {R}iemann surface into a flag manifold }, Journal = { J. Differential Geom. }, Volume = { 43 }, Pages = { 99--118 }, Year = { 1996 } } @Article{ Hvi89, Author = { M.D. Hvidsten }, Title = { {V}olume and energy stability for isometric minimal immersions }, Journal = { Illinois J. Math. }, Volume = { 33 }, Pages = { 488-494 }, Year = { 1989 } } @Article{ HviTon72, Author = { M.D. Hvidsten and P. Tondeur }, Title = { {M}inimal submanifolds and convex functions }, Journal = { T\^ohoku Math.\ J. }, Volume = { 24 }, Pages = { 571-579 }, Year = { 1972 } } @Article{ HviTon86, Author = { M.D. Hvidsten and P. Tondeur }, Title = { {A} characterization of harmonic foliations by variations of the metric }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 98 }, Pages = { 359-362 }, Year = { 1986 } } @Article{ Hwa88, Author = { J.F. Hwang }, Title = { {C}omparison principles and {L}iouville theorems for prescribed mean curvature equations in unbounded domain }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 3 }, Pages = { 341-355 }, Year = { 1988 } } @Article{ Hwa94, Author = { J.F. Hwang }, Title = { {G}rowth properties for the minimal surface equation in unbounded domains }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 121 }, Pages = { 1027-1037 }, Year = { 1994 } } @Unpublished{ Hyd86, Author = { S. Hyde }, Title = { {T}riply periodic minimal surfaces and crystallography }, Note = { Thesis. Canberra }, Year = { 1986 } } @Article{ HydLid87, Author = { S.T. Hyde and S. Lidin }, Title = { {A} construction algorithm for minimal surfaces }, Journal = { J. Physique }, Volume = { 48 }, Pages = { 1585-1590 }, Year = { 1987 } } @Unpublished{ Hel, Author = { F. H{\'e}lein }, Title = { {D}iff\'eomorphismes harmoniques, formule de la coaire et calibrations }, Note = { preprint } } @Misc{ HelA, Author = { F. H{\'e}lein }, Title = { {E}coulement stationnaire et irrotationel d'un fluide incompressible dans un canal bidimensionnel {\`a} fond presque plat } } @Article{ HelB, Author = { F. H{\'e}lein }, Title = { {I}n{\'e}galit{\'e} isoperim{\'e}trique et calibration }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) } } @Unpublished{ HelC, Author = { F. H{\'e}lein }, Title = { {P}robl\`eme de {D}irichlet pour les applications harmoniques avec donn\'ees aux bords constantes }, Note = { preprint } } @Article{ Hel87, Author = { F. H{\'e}lein }, Title = { {M}inima de la fonctionnelle \'energie libre des cristaux liquides }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 305 }, Pages = { 565-568 }, Year = { 1987 } } @Article{ Hel88, Author = { F. H{\'e}lein }, Title = { {H}om\'eomorphismes quasi conformes entre surfaces riemanniennes }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 307 }, Pages = { 725-730 }, Year = { 1988 } } @Article{ Hel88A, Author = { F. H{\'e}lein }, Title = { {R}egularity and uniqueness of harmonic maps into an ellipsoid }, Journal = { Manuscripta Math. }, Volume = { 60 }, Pages = { 235-257 }, Year = { 1988 } } @Unpublished{ Hel89, Author = { F. H{\'e}lein }, Title = { {A}pplications harmoniques et applications minimisantes entre vari\'et\'es riemanniennes }, Note = { Th\`ese. Ecole Polytechnique }, Year = { 1989 } } @Article{ Hel89A, Author = { F. H{\'e}lein }, Title = { {A}pproximations of {S}obolev maps between an open set and an {E}uclidean sphere, boundary data, and singularities }, Journal = { Math.\ Ann. }, Volume = { 285 }, Pages = { 125-140 }, Year = { 1989 } } @Article{ Hel89B, Author = { F. H{\'e}lein }, Title = { {D}iff\'eomorphismes harmoniques entre un ouvert de {${\bf {R}}^3$} et une vari\'et\'e riemannienne }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 308 }, Pages = { 237-240 }, Year = { 1989 } } @Article{ Hel89C, Author = { F. H{\'e}lein }, Title = { {M}inimizing harmonic maps, harmonic diffeomorphisms and rotational symmetry }, Journal = { Compositio Math. }, Volume = { 69 }, Pages = { 175-228 }, Year = { 1989 } } @Incollection{ Hel90, Author = { F. H{\'e}lein }, Title = { {H}armonic diffeomorphisms between {R}iemannian manifolds }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 309-318 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Article{ Hel90A, Author = { F. H{\'e}lein }, Title = { {R}\'egularit\'e des applications faiblement harmoniques entre une surface et une sph\`ere }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 311 }, Pages = { 519-524 }, Year = { 1990 } } @Article{ Hel91, Author = { F. H{\'e}lein }, Title = { {H}armonic diffeomorphisms with rotational symmetries }, Journal = { J. Reine Angew.\ Math. }, Volume = { 414 }, Pages = { 45-49 }, Year = { 1991 } } @Article{ Hel91A, Author = { F. H{\'e}lein }, Title = { {R}egularity of weakly harmonic maps from a surface into a manifold with symmetries }, Journal = { Manuscripta Math. }, Volume = { 70 }, Pages = { 203-218 }, Year = { 1991 } } @Article{ Hel91B, Author = { F. H{\'e}lein }, Title = { {R}\'egularit\'e des applications faiblement harmoniques entre une surface et une vari\'et\'e riemannienne }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 312 }, Pages = { 591-596 }, Year = { 1991 } } @Article{ Hel92, Author = { F. H{\'e}lein }, Title = { {O}n weakly harmonic maps and {N}oether harmonic maps from a {R}iemann surface into a {R}iemannian manifold }, Journal = { Banach Center Publ. }, Volume = { 27 }, Pages = { 175-181 }, Year = { 1992 } } @Book{ Hel96, Author = { F. H{\'e}lein }, Title = { {A}pplications harmoniques, lois de conservation et rep{\`e}res mobiles }, Publisher = { Diderot Editeur }, Address = { Paris }, Year = { 1996 } } @Article{ IanVis86, Author = { S. Ianus and M. Visinescu }, Title = { {S}pontaneous compactification induced by nonlinear scalar dynamics, gauge fields and submersions }, Journal = { Classical Quantum Gravity }, Volume = { 3 }, Pages = { 889-896 }, Year = { 1986 } } @Article{ IanVis87, Author = { S. Ianus and M. Visinescu }, Title = { {K}aluza-{K}lein theory with scalar fields and generalized {H}opf manifolds }, Journal = { Classical Quantum Gravity }, Volume = { 4 }, Pages = { 1317-1325 }, Year = { 1987 } } @Article{ Ii72, Author = { K. Ii }, Title = { {M}inimal submanifolds and convex functions }, Journal = { T\^ohoku Math.\ J. }, Volume = { 24 }, Pages = { 571-579 }, Year = { 1972 } } @Article{ Ika92, Author = { O. Ikawa }, Title = { {O}n stability of a certain minimal submanifold in {${S}{U}(3)/{S}{O}(3)$} }, Journal = { Tsukuba J. Math. }, Volume = { 16 }, Pages = { 335-352 }, Year = { 1992 } } @Article{ Ika93, Author = { O. Ikawa }, Title = { {E}quivariant minimal immersions of compact {R}iemannian homogeneous spaces into compact {R}iemannian homogeneous spaces }, Journal = { Tsukuba J. Math. }, Volume = { 17 }, Pages = { 169-188 }, Year = { 1993 } } @Article{ Ika93A, Author = { O. Ikawa }, Title = { {H}armonic mappings, minimal and totally geodesic immersions of compact {R}iemannian homegeneous spaces into {G}rassmann manifolds }, Journal = { Kodai Math.\ J. }, Volume = { 16 }, Pages = { 295-305 }, Year = { 1993 } } @Article{ Ike88, Author = { T. Ikegami }, Title = { {O}n the boundary behaviour of harmonic morphisms at the boundary of compactifications of {M}artin type }, Journal = { Osaka J. Math. }, Volume = { 25 }, Pages = { 729-736 }, Year = { 1988 } } @Unpublished{ Ili, Author = { S. Ilias }, Title = { {Q}uelques r\'esultats d'isolement pour les applications harmoniques }, Note = { Univ. Tours, preprint } } @Article{ Ili96, Author = { S. Ilias }, Title = { {I}n\'egalit\'es de {S}obolev et r\'esultats d'isolement pour les applications harmoniques }, Journal = { J. Funct.\ Anal. }, Volume = { 139 }, Pages = { 182--195 }, Year = { 1996 } } @Incollection{ Ilm93, Author = { T. Ilmanen }, Title = { {T}he level-set flow on a manifold }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 193-204 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ Ima75, Author = { H. Imai }, Title = { {T}he value distribution of harmonic mappings between {R}iemannian {$n$}-space }, Journal = { Nagoya Math.\ J. }, Volume = { 59 }, Pages = { 45-58 }, Year = { 1975 } } @Article{ Ino92, Author = { Y. Inoue }, Title = { {T}wistor spaces of even dimensional {R}iemannian manifolds }, Journal = { J. Math.\ Kyoto Univ. }, Volume = { 32 }, Pages = { 101-134 }, Year = { 1992 } } @Article{ Ish95, Author = { M. Ishida }, Title = { {T}he existence of {$p$}-harmonic maps between spheres }, Journal = { Math.\ J. Okayama Univ. }, Volume = { 37 }, Pages = { 187--200 }, Year = { 1995 } } @Article{ IshIsh75, Author = { S. Ishihara and T. Ishihara }, Title = { {N}otes on relatively harmonic immersions }, Journal = { Hokkaido Math.\ J. }, Volume = { 4 }, Pages = { 234-246 }, Year = { 1975 } } @Article{ IshYan71, Author = { S. Ishihara and K. Yano }, Title = { {S}ubmanifolds with parallel mean curvature vector }, Journal = { J. Differential Geom. }, Volume = { 6 }, Pages = { 95-118 }, Year = { 1971 } } @Article{ IshYan75, Author = { S. Ishihara and K. Yano }, Title = { {H}armonic and relatively affine mappings }, Journal = { J. Differential Geom. }, Volume = { 10 }, Pages = { 501-509 }, Year = { 1975 } } @Misc{ Ish, Author = { T. Ishihara }, Title = { {C}omplete nonorientable minimal surfaces in {${\bf {R}}^3$} } } @Misc{ IshA, Author = { T. Ishihara }, Title = { {T}he {G}auss map of immersions into self-immersed manifolds } } @Misc{ IshB, Author = { T. Ishihara }, Title = { {T}he {G}auss map of pseudo-{R}iemannian immersions in submanifolds of pseudo-{E}uclidean spaces } } @Article{ Ish71, Author = { T. Ishihara }, Title = { {A} remark on harmonic quasiconformal mappings }, Journal = { J. Math.\ Tokushima Univ. }, Volume = { 5 }, Pages = { 17-23 }, Year = { 1971 } } @Article{ Ish77, Author = { T. Ishihara }, Title = { {T}he index of a holomorphic mapping and the index theorem }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 66 }, Pages = { 169-174 }, Year = { 1977 } } @Article{ Ish79, Author = { T. Ishihara }, Title = { {H}armonic sections of tangent bundles }, Journal = { J. Math.\ Tokushima Univ. }, Volume = { 13 }, Pages = { 23-27 }, Year = { 1979 } } @Article{ Ish79A, Author = { T. Ishihara }, Title = { {A} mapping of {R}iemannian manifolds which preserves harmonic functions }, Journal = { J. Math.\ Kyoto Univ. }, Volume = { 19 }, Pages = { 215-229 }, Year = { 1979 } } @Article{ Ish82, Author = { T. Ishihara }, Title = { {T}he harmonic {G}auss maps in a generalized sense }, Journal = { J. London Math.\ Soc. }, Volume = { 26 }, Pages = { 104-112 }, Year = { 1982 } } @Article{ Ish83, Author = { T. Ishihara }, Title = { {T}he {G}auss map and non-holomorphic harmonic maps }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 89 }, Pages = { 661-665 }, Year = { 1983 } } @Article{ Ish83A, Author = { T. Ishihara }, Title = { {T}he {G}auss map of {K}\"ahler immersions into complex hyperbolic spaces }, Journal = { J. Math.\ Tokushima Univ. }, Volume = { 17 }, Pages = { 11-14 }, Year = { 1983 } } @Article{ Ish88, Author = { T. Ishihara }, Title = { {M}aximal spacelike submanifolds of a pseudoriemannian space of constant curvature }, Journal = { Michigan Math.\ J. }, Volume = { 35 }, Pages = { 345-352 }, Year = { 1988 } } @Article{ Ish89, Author = { T. Ishihara }, Title = { {C}omplete {M}\"obius strips minimally immersed in {${\bf {R}}^3$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 107 }, Pages = { 803-806 }, Year = { 1989 } } @Article{ Ish93, Author = { T. Ishihara }, Title = { {H}armonic maps of non-orientable surfaces to four dimensional manifolds }, Journal = { T\^ohoku Math.\ J. }, Volume = { 45 }, Pages = { 1-12 }, Year = { 1993 } } @Article{ Ish93A, Author = { T. Ishihara }, Title = { {H}armonic maps of nonorientable surfaces to four-manifolds }, Journal = { T\^ohoku Math.\ J. }, Volume = { 45 }, Pages = { 1-12 }, Year = { 1993 } } @Article{ Ish94, Author = { T. Ishihara }, Title = { {H}armonic maps of nonorientable surfaces into complex {G}rassmann manifolds }, Journal = { J. Math.\ Tokushima Univ. }, Volume = { 28 }, Pages = { 29-37 }, Year = { 1994 } } @Misc{ IshC, Author = { S. Ishikawa }, Title = { {S}ome properties of generalized {G}auss maps } } @Article{ Ish82A, Author = { S. Ishikawa }, Title = { {O}n some extensions of the {R}uh-{V}ilms theorem }, Journal = { Tensor (N.S.) }, Volume = { 39 }, Pages = { 113-116 }, Year = { 1982 } } @Article{ Ish88A, Author = { S. Ishikawa }, Title = { {O}n {G}auss maps of immersions into space form }, Journal = { Rep.\ Fac.\ Sci.\ Engrg.\ Saga Univ.\ Math. }, Volume = { 16 }, Pages = { 1-11 }, Year = { 1988 } } @Article{ Iso97, Author = { T. Isobe }, Title = { {O}ptimal regularity of harmonic maps from a {R}iemannian manifold into a static {L}orentzian manifold }, Journal = { Pacific J. Math. }, Volume = { 178 }, Pages = { 71--93 }, Year = { 1997 } } @Incollection{ Ito93, Author = { M. Itoh }, Title = { {H}iggs fields and harmonic maps }, Booktitle = { {G}eometry and its applications }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 59-71 }, Year = { 1993 } } @Article{ ItoMan89, Author = { M. Itoh and H. Manabe }, Title = { {Y}ang--{M}ills--{H}iggs fields and harmonicity of limit maps }, Journal = { Proc.\ Japan Acad.\ Ser.\ A Math.\ Sci. }, Volume = { 65 }, Pages = { 113-115 }, Year = { 1989 } } @Misc{ ItoMur, Author = { M. Itoh and S. Murakami }, Title = { {F}latness of holomorphic connections } } @Article{ Ito70, Author = { T. Itoh }, Title = { {C}omplete constant mean curvature surfaces in {${E}^4$} }, Journal = { Kodai Math.\ Sem. }, Volume = { 22 }, Pages = { 150-158 }, Year = { 1970 } } @Article{ Ito73, Author = { T. Itoh }, Title = { {M}inimal surfaces in a {R}iemannian manifold of constant curvature }, Journal = { Kodai Math.\ Sem. }, Volume = { 25 }, Pages = { 202-214 }, Year = { 1973 } } @Article{ Ito88, Author = { T. Itoh }, Title = { {A} characterization of the generalized {V}eronese surface }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 104 }, Pages = { 571-576 }, Year = { 1988 } } @Article{ Ito88A, Author = { T. Itoh }, Title = { {I}sotropic minimal submanifolds in a space form }, Journal = { Tsukuba J. Math. }, Volume = { 12 }, Pages = { 497-505 }, Year = { 1988 } } @Incollection{ Iva86, Author = { A.O. Ivanov }, Title = { {G}lobally minimal symmetric surfaces in a {E}uclidean space }, Booktitle = { {G}eometry, differential equations and mechanics ({M}oscow 1985) }, Publisher = { Moscow State Univ.\ Mekh.-Mat.\ Fak. }, Address = { Moscow }, Pages = { 69-71 }, Note = { (Russian) }, Year = { 1986 } } @Article{ Iva90, Author = { A.O. Ivanov }, Title = { {G}auge forms and new examples of stable and globally minimal surfaces }, Journal = { Mat.\ Sb. }, Pages = { 1443-1463 }, Note = { (Russian) }, Year = { 1990 } } @Article{ Iva92, Author = { T.A. Ivanova }, Title = { {E}uler equations in models of theoretical physics }, Journal = { Mat.\ Zametki }, Volume = { 52 }, Pages = { 44-52, 156 }, Year = { 1992 } } @Article{ Iva93, Author = { T.A. Ivanova }, Title = { {O}ctonians, self-duality and strings }, Journal = { Phys.\ Lett.\ B }, Volume = { 315 }, Pages = { 277-228 }, Year = { 1993 } } @Unpublished{ IveLan95, Author = { T. Ivey and J.M. Landsberg }, Title = { {O}n minimal isometric embeddings }, Note = { Preprint }, Year = { 1995 } } @Incollection{ i88, Author = { O.V. Ogievetski{\u i} }, Title = { {H}armonic representatives of instantons and self-dual monopoles }, Booktitle = { {G}roup theoretical methods in physics ({V}arna 1987) }, Publisher = { Springer }, Address = { Berlin }, Volume = { 313 }, Pages = { 548-554 }, Series = { Lecture Notes in Phys. }, Year = { 1988 } } @Article{ ima85, Author = { I.A. Ta{\u i}manov }, Title = { {C}losed geodesics on non simply-connected manifolds }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 40 }, Pages = { 157-158 }, Year = { 1985 } } @Article{ JacOsb82, Author = { I. Jack and H. Osborn }, Title = { {G}reen functions for the {D}irac equation for general classical solutions of the {${C}{P}^{n-1}$} model }, Journal = { J. Phys.\ A }, Volume = { 15 }, Pages = { 245-252 }, Year = { 1982 } } @Article{ JacRub88, Author = { W. Jaco and J.H. Rubinstein }, Title = { {${P}{L}$} minimal surfaces in {$3$}-manifolds }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 493-524 }, Year = { 1988 } } @Article{ JacSai87, Author = { M. Jacques and Y. Saint-Aubin }, Title = { {I}nfinite dimensional {L}ie algebras acting on the solution space of various {$\sigma$}-models }, Journal = { J. Math.\ Phys. }, Volume = { 28 }, Pages = { 2463-2479 }, Year = { 1987 } } @Article{ Jag94, Author = { C. Jaggy }, Title = { {O}n the classification of constant mean curvature tori in {${\bf {R}}^3$} }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 69 }, Pages = { 640-658 }, Year = { 1994 } } @Article{ JenSer68, Author = { H. Jenkins and J. Serrin }, Title = { {T}he {D}irichlet problem for the minimal surface equation in higher dimensions }, Journal = { J. Reine Angew.\ Math. }, Volume = { 229 }, Pages = { 170-187 }, Year = { 1968 } } @Misc{ JenLia, Author = { G.R. Jensen and R. Liao }, Title = { {T}otally real, flat minimal surfaces in complex projective space } } @Article{ JenLia95, Author = { G.R. Jensen and R.J. Liao }, Title = { {F}amilies of flat minimal tori in {${\bf {{C}}}{{P}}^n$} }, Journal = { J. Differential Geom. }, Volume = { 42 }, Pages = { 113-132 }, Year = { 1995 } } @Article{ JenRig90, Author = { G.R. Jensen and M. Rigoli }, Title = { {N}eutral surfaces in neutral 4-spaces }, Journal = { Matematiche (Catania) }, Volume = { 45 }, Pages = { 407-443 }, Year = { 1990 } } @Misc{ JenRig, Author = { G. Jensen and M. Rigoli }, Title = { {C}odazzi surfaces in {$4$}-manifolds } } @Incollection{ JenRigA, Author = { G. Jensen and M. Rigoli }, Title = { {H}armonic maps, twistor spaces, and twistor lifts }, Booktitle = { {P}roc. {C}onf. sur les espaces fibr{\'e}s et leur utilization en {P}hysique }, Editor = { J.T. Ezin and A. Verjovski }, Publisher = { World Scientific }, Address = { Singapore } } @Unpublished{ JenRigB, Author = { G. Jensen and M. Rigoli }, Title = { {L}agrangian surfaces in {K}\"ahler--{E}instein surfaces }, Note = { Preprint } } @Misc{ JenRigC, Author = { G. Jensen and M. Rigoli }, Title = { {Q}uantization of curvature of harmonic two spheres into complex projective space } } @Incollection{ JenRig83, Author = { G. Jensen and M. Rigoli }, Title = { {A} class of harmonic maps into real {G}rassmannians }, Booktitle = { {D}ifferential {G}eometry on {H}omogeneous {S}paces, {T}orino 1983 }, Pages = { 99-116 }, Series = { Rend.\ Sem.\ Mat.\ Univ.\ Politec.\ Torino }, Year = { 1983 } } @Incollection{ JenRig83A, Author = { G. Jensen and M. Rigoli }, Title = { {M}inimal surfaces in spheres }, Booktitle = { {D}ifferential {G}eometry on {H}omogeneous {S}paces, {T}orino 1983 }, Pages = { 75-98 }, Series = { Rend.\ Sem.\ Mat.\ Univ.\ Politec.\ Torino }, Year = { 1983 } } @Article{ JenRig83B, Author = { G. Jensen and M. Rigoli }, Title = { {M}inimal surfaces in spheres by the method of moving frames }, Journal = { S\'em.\ Geom.\ Diff.\ Nancy }, Year = { 1983 } } @Article{ JenRig88, Author = { G. Jensen and M. Rigoli }, Title = { {H}armonically immersed surfaces of {${\bf {R}}^n$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 307 }, Pages = { 363-372 }, Year = { 1988 } } @Article{ JenRig89, Author = { G. Jensen and M. Rigoli }, Title = { {H}armonically immersed surfaces of {${\bf {R}}^n$} (correction) }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 311 }, Pages = { 425-428 }, Year = { 1989 } } @Article{ JenRig89A, Author = { G. Jensen and M. Rigoli }, Title = { {H}armonic {G}auss maps }, Journal = { Pacific J. Math. }, Volume = { 136 }, Pages = { 261-282 }, Year = { 1989 } } @Article{ JenRig89B, Author = { G. Jensen and M. Rigoli }, Title = { {O}n the isotropy of compact minimal surfaces in {${C}{P}^n$} }, Journal = { Math.\ Z. }, Volume = { 200 }, Pages = { 169-180 }, Year = { 1989 } } @Incollection{ JenRig89C, Author = { G. Jensen and M. Rigoli }, Title = { {T}wistor and {G}auss lifts of surfaces in four-manifolds }, Booktitle = { {R}ecent developments in geometry }, Editor = { S.Y. Cheng and H. Choi and R.E. Greene }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 101 }, Pages = { 197-232 }, Series = { Contemp.\ Math. }, Year = { 1989 } } @Article{ JenRigYan87, Author = { G. Jensen and M. Rigoli and K. Yang }, Title = { {H}olomorphic curves in the complex quadric }, Journal = { Bull.\ Austral.\ Math.\ Soc. }, Volume = { 35 }, Pages = { 125-148 }, Year = { 1987 } } @Article{ Jeo94, Author = { M.J. Jeon }, Title = { {C}onstruction of harmonic maps between pseudospheres }, Journal = { J. Korean Math.\ Soc. }, Volume = { 31 }, Pages = { 157-167 }, Year = { 1994 } } @Article{ Jeo95, Author = { M.J. Jeon }, Title = { {E}xistence of homotopic harmonic maps into metric space of nonpositive curvature }, Journal = { Comm.\ Korean Math.\ Soc. }, Volume = { 10 }, Pages = { 931--941 }, Year = { 1995 } } @Article{ Jhi92, Author = { Z.R. Jhi }, Title = { {L}iouville theorems for harmonic maps }, Journal = { Invent.\ Math. }, Volume = { 108 }, Pages = { 1-10 }, Year = { 1992 } } @Article{ Ji, Author = { M. Ji }, Title = { {M}inimal annuli in {R}iemannian manifolds }, Journal = { Acta Math.\ Sinica } } @Misc{ JiA, Author = { M. Ji }, Title = { {M}ultiple solution to the {D}ouglas problem in {${S}^n$} } } @Unpublished{ Ji87, Author = { M. Ji }, Title = { {M}inimal surfaces in {R}iemannian manifolds }, Note = { Thesis. Acad. Sinica }, Year = { 1987 } } @Article{ Ji89, Author = { M. Ji }, Title = { {A}n apriori estimate for {D}ouglas problem in {R}iemannian manifolds }, Journal = { Acta Math.\ Sinica (N.S.) }, Pages = { 235-249 }, Year = { 1989 } } @Article{ Ji89A, Author = { M. Ji }, Title = { {M}inimal surfaces of {R}iemannian manifolds }, Journal = { Chinese Sci.\ Bull. }, Volume = { 34 }, Pages = { 444-447 }, Year = { 1989 } } @Article{ Ji89B, Author = { M. Ji }, Title = { {A} remark on perturbation method }, Journal = { Acta Math.\ Sinica }, Volume = { 32 }, Pages = { 628-631 }, Year = { 1989 } } @Misc{ JiWan, Author = { M. Ji and G.Y. Wang }, Title = { {G}eneralized {L}justernik--{S}chnirelmann theories for {L}ie group actions with an application to the {P}lateau problem } } @Book{ JiWan93, Author = { M. Ji and G.Y. Wang }, Title = { {M}inimal surfaces in {R}iemannian manifolds }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 495 }, Series = { Mem.\ Amer.\ Math.\ Soc. }, Year = { 1993 } } @Article{ Jia83, Author = { G.Y. Jiang }, Title = { {H}armonic and totally geodesic mappings }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 4 }, Pages = { 577-586 }, Note = { (Chinese) }, Year = { 1983 } } @Article{ Jia84, Author = { G.Y. Jiang }, Title = { {C}urvature restrictions on a minimal submanifold with constant curvature immersed in a manifold with constant positive curvature }, Journal = { J. Fudan Univ.\ Natur.\ Sci. }, Volume = { 23 }, Pages = { 171-178 }, Note = { (Chinese with English summary) }, Year = { 1984 } } @Article{ Jia85, Author = { G.Y. Jiang }, Title = { {R}elatively harmonic mappings and variations of smooth mappings }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 6 }, Pages = { 103-114 }, Note = { (Chinese) }, Year = { 1985 } } @Article{ Jia86, Author = { G.Y. Jiang }, Title = { {$2$}-harmonic isometric immersions between {R}iemannian manifolds }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 7 }, Pages = { 130-144 }, Note = { (Chinese) }, Year = { 1986 } } @Article{ Jia86A, Author = { G.Y. Jiang }, Title = { {$2$}-harmonic maps and their first and second variational formulas }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 7 }, Pages = { 389-402 }, Note = { (Chinese) }, Year = { 1986 } } @Article{ Jia87, Author = { G.Y. Jiang }, Title = { {T}he conservation law for {$2$}-harmonic maps between {R}iemannian manifolds }, Journal = { Acta Math.\ Sinica }, Volume = { 30 }, Pages = { 220-225 }, Note = { (Chinese) }, Year = { 1987 } } @Article{ Jia87A, Author = { G.Y. Jiang }, Title = { {S}ome nonexistence theorems on {$2$}-harmonic and isometric immersions in {E}uclidean space }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 8 }, Pages = { 377-383 }, Note = { (Chinese) }, Year = { 1987 } } @Article{ Jia96, Author = { G.Y. Jiang }, Title = { {I}dentity maps and harmonic maps }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 17 }, Pages = { 285--294 }, Note = { (Chinese) }, Year = { 1996 } } @Article{ Jin, Author = { Z. Jin }, Title = { {L}iouville theorem for harmonic maps }, Journal = { Invent.\ Math. } } @Article{ JinKaz91, Author = { Z. Jin and J.L. Kazdan }, Title = { {O}n the rank of harmonic maps }, Journal = { Math.\ Z. }, Volume = { 207 }, Pages = { 535-537 }, Year = { 1991 } } @Article{ Joh91, Author = { G.D. Johnson }, Title = { {A}n intrinsic characterization of a class of minimal surfaces in constant curvature manifolds }, Journal = { Pacific J. Math. }, Volume = { 113 }, Pages = { 1041-1044 }, Year = { 1991 } } @Article{ Jon79, Author = { P.W. Jones }, Title = { {A} complete bounded complex submanifold of {${\bf {C}}^3$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 76 }, Pages = { 305-306 }, Year = { 1979 } } @Article{ JorMee83, Author = { L. Jorge and W.H. Meeks }, Title = { {T}he topology of complete minimal surfaces of finite total {G}aussian curvature }, Journal = { Topology }, Volume = { 22 }, Pages = { 203-221 }, Year = { 1983 } } @Article{ JorMer84, Author = { L. Jorge and F. Mercuri }, Title = { {M}inimal immersions into space forms with two principal curvatures }, Journal = { Math.\ Z. }, Volume = { 187 }, Pages = { 325-333 }, Year = { 1984 } } @Article{ JorXav80, Author = { L. Jorge and F. Xavier }, Title = { {A} complete minimal surface in {${\bf {R}}^3$} between two parallel planes }, Journal = { Ann.\ of Math. }, Volume = { 12 }, Pages = { 204-206 }, Year = { 1980 } } @Article{ JorXav81, Author = { L. Jorge and F. Xavier }, Title = { {A}n inequality between the exterior diameter and the mean curvature of bounded immersion }, Journal = { Math.\ Z. }, Volume = { 178 }, Pages = { 77-82 }, Year = { 1981 } } @Misc{ Jos, Author = { J. Jost }, Title = { {G}eneralized harmonic maps between metric spaces } } @Misc{ JosA, Author = { J. Jost }, Title = { {S}trings with boundary: {A} quantization of {P}lateau's problem } } @Article{ Jos80, Author = { J. Jost }, Title = { {E}ine geometrische {B}emerkung zur {S}\"atzen \"uber harmonische {A}bbildungen, die ein {D}irichletproblem l\"osen }, Journal = { Manuscripta Math. }, Volume = { 32 }, Pages = { 51-57 }, Year = { 1980 } } @Book{ Jos81, Author = { J. Jost }, Title = { {E}indeutigkeit harmonischer {A}bbildungen zwischen {R}iemannschen {F}l\"achen }, Publisher = { Univ.\ Bonn }, Address = { Bonn }, Volume = { 129 }, Series = { Bonner Math.\ Schriften }, Year = { 1981 } } @Article{ Jos81A, Author = { J. Jost }, Title = { {E}in {E}xistenzbeweis f\"ur harmonische {A}bbildungen, die ein {D}irichletproblem l\"osen, mittels der {M}ethode des {W}\"armeflusses }, Journal = { Manuscripta Math. }, Volume = { 34 }, Pages = { 17-25 }, Year = { 1981 } } @Article{ Jos81B, Author = { J. Jost }, Title = { {U}nivalency of harmonic mappings between surfaces }, Journal = { J. Reine Angew.\ Math. }, Volume = { 324 }, Pages = { 141-153 }, Year = { 1981 } } @Article{ Jos82, Author = { J. Jost }, Title = { {A} maximum principle for harmonic mappings which solve a {D}irichlet problem }, Journal = { Manuscripta Math. }, Volume = { 38 }, Pages = { 129-130 }, Year = { 1982 } } @Article{ Jos83, Author = { J. Jost }, Title = { {E}xistence proofs for harmonic mappings with the help of a maximum principle }, Journal = { Math.\ Z. }, Volume = { 184 }, Pages = { 489-496 }, Year = { 1983 } } @Incollection{ Jos83A, Author = { J. Jost }, Title = { {H}armonic mappings between {R}iemannian manifolds }, Booktitle = { {P}roc. {C}entre {M}ath. {A}nalysis }, Publisher = { A.N.U. Press }, Address = { Canberra }, Year = { 1983 } } @Article{ Jos84, Author = { J. Jost }, Title = { {T}he {D}irichlet problem for harmonic maps from a surface with boundary onto a {$2$}-sphere with nonconstant boundary values }, Journal = { J. Differential Geom. }, Volume = { 19 }, Pages = { 393-401 }, Year = { 1984 } } @Unpublished{ Jos84A, Author = { J. Jost }, Title = { {G}lobal {V}ariationsmethoden in der {T}heorie der harmonischen und konformen {A}bbildungen in zwei {D}imensionen nebst {A}nwendungen auf {M}inimalfl\"achers }, Note = { Bonn Habitat. Thesis }, Year = { 1984 } } @Book{ Jos84B, Author = { J. Jost }, Title = { {H}armonic maps between surfaces }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1062 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ Jos85, Author = { J. Jost }, Title = { {C}onformal mappings and the {P}lateau--{D}ouglas problem in {R}iemannian manifolds }, Journal = { J. Reine Angew.\ Math. }, Volume = { 359 }, Pages = { 37-54 }, Year = { 1985 } } @Incollection{ Jos85A, Author = { J. Jost }, Title = { {L}ectures on harmonic maps }, Booktitle = { {H}armonic {M}appings and {M}inimal {I}mmersions, {M}ontecatini 1984 }, Editor = { E. Giusti }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1161 }, Pages = { 118-192 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Article{ Jos85B, Author = { J. Jost }, Title = { {A} note on harmonic maps between surfaces }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 2 }, Pages = { 397-405 }, Year = { 1985 } } @Article{ Jos86, Author = { J. Jost }, Title = { {E}xistence results for embedded minimal surfaces of controlled topological type, {I} }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 13 }, Pages = { 15-50 }, Year = { 1986 } } @Article{ Jos86A, Author = { J. Jost }, Title = { {E}xistence results for embedded minimal surfaces of controlled topological type, {I}{I} }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 13 }, Pages = { 401-426 }, Year = { 1986 } } @Article{ Jos86B, Author = { J. Jost }, Title = { {O}n the existence of harmonic maps from a surface into the real projective plane }, Journal = { Compositio Math. }, Volume = { 59 }, Pages = { 15-19 }, Year = { 1986 } } @Article{ Jos86C, Author = { J. Jost }, Title = { {O}n the regularity of minimal surfaces with free boundaries in {R}iemannian manifolds }, Journal = { Manuscripta Math. }, Volume = { 56 }, Pages = { 279-291 }, Year = { 1986 } } @Incollection{ Jos86D, Author = { J. Jost }, Title = { {T}wo-dimensional geometric variational problems }, Booktitle = { {P}roc. {I}nternat. {C}ongress of {M}ath. ({B}erkeley, {C}alif. 1986) }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Pages = { 1180-1189 }, Year = { 1986 } } @Article{ Jos87, Author = { J. Jost }, Title = { {C}ontinuity of minimal surfaces with piecewise smooth free boundaries }, Journal = { Math.\ Ann. }, Volume = { 276 }, Pages = { 599-614 }, Year = { 1987 } } @Article{ Jos87A, Author = { J. Jost }, Title = { {E}xistence results for embedded minimal surfaces of controlled topological type, {I}{I}{I} }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 14 }, Pages = { 165-167 }, Year = { 1987 } } @Incollection{ Jos87B, Author = { J. Jost }, Title = { {O}n the existence of embedded minimal surfaces of higher genus with free boundaries in {R}iemannian manifolds }, Booktitle = { {V}ariational methods for free surface interfaces }, Editor = { P. Concus and R. Finn }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Pages = { 65-75 }, Year = { 1987 } } @Article{ Jos88, Author = { J. Jost }, Title = { {E}mbedded minimal disks with a free boundary on a polyhedron in {${\bf {R}}^3$} }, Journal = { Math.\ Z. }, Volume = { 199 }, Pages = { 311-320 }, Year = { 1988 } } @Article{ Jos88A, Author = { J. Jost }, Title = { {D}as {E}xistenzproblem f\"ur {M}inimalfl\"achen }, Journal = { J. Deutsch.\ Math.\ Verein. }, Volume = { 91 }, Pages = { 1-32 }, Year = { 1988 } } @Article{ Jos88B, Author = { J. Jost }, Title = { {T}he geometric calculus of variations: {A} short survey and a list of open problems }, Journal = { Exposition.\ Math. }, Volume = { 6 }, Pages = { 111-143 }, Year = { 1988 } } @Incollection{ Jos88C, Author = { J. Jost }, Title = { {H}armonic maps -- {A}nalytic theory and geometric significance }, Booktitle = { {P}artial differential equations and the calculus of variations }, Editor = { S. Hildebrandt and R. Leis }, Volume = { 1357 }, Pages = { 264-296 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Book{ Jos88D, Author = { J. Jost }, Title = { {N}onlinear methods in {R}iemannian and {K}\"ahlerian geometry }, Publisher = { Birkh\"auser }, Volume = { 10 }, Series = { DMV Sem. }, Year = { 1988 } } @Article{ Jos89, Author = { J. Jost }, Title = { {E}mbedded minimal surfaces in manifolds diffeomorphic to the three-dimensional ball or sphere }, Journal = { J. Differential Geom. }, Volume = { 30 }, Pages = { 555-577 }, Year = { 1989 } } @Article{ Jos89A, Author = { J. Jost }, Title = { {A} nonparametric proof of the theorem of {L}usternik and {S}chnirelmann }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 53 }, Pages = { 497-505 }, Note = { (Correction in Arch. Math. 56 (1991) 624) }, Year = { 1989 } } @Article{ Jos91, Author = { J. Jost }, Title = { {H}armonic maps and curvature computations in {T}eichm\"uller theory }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { 16 }, Pages = { 13-46 }, Year = { 1991 } } @Book{ Jos91A, Author = { J. Jost }, Title = { {T}wo-dimensional geometric variational problems }, Publisher = { Wiley }, Year = { 1991 } } @Book{ Jos93, Author = { J. Jost }, Title = { {M}inimal {S}urfaces and {T}eichm{\"u}ller {T}heory }, Publisher = { Universit{\"a}t Bonn }, Address = { Bonn }, Volume = { 1993:31 }, Series = { Vorlesungsreihe SFB 256 }, Year = { 1993 } } @Incollection{ Jos93A, Author = { J. Jost }, Title = { {U}nstable solutions of two dimensional geometric variational problems }, Booktitle = { {D}ifferential {G}eometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 54 }, Pages = { 205-244 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1993 } } @Article{ Jos94, Author = { J. Jost }, Title = { {E}quilibrium maps between metric spaces }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 2 }, Pages = { 173-204 }, Year = { 1994 } } @Article{ Jos95, Author = { J. Jost }, Title = { {C}onvex functionals and generalized harmonic maps into spaces of non positive curvature }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 70 }, Pages = { 659-673 }, Year = { 1995 } } @Incollection{ Jos96, Author = { J. Jost }, Title = { {O}rientable and nonorientable minimal surfaces }, Booktitle = { {W}orld {C}ongress of {N}onlinear {A}nalysts '92, {V}ol. {I}-{I}{V} ({T}ampa, {F}{L}, 1992) }, Publisher = { de Gruyter }, Address = { Berlin }, Pages = { 819-826 }, Year = { 1996 } } @Article{ Jos97, Author = { J. Jost }, Title = { {G}eneralized {D}irichlet forms and harmonic maps }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 5 }, Pages = { 1--19 }, Year = { 1997 } } @Article{ JosKar82, Author = { J. Jost and H. Karcher }, Title = { {G}eometrische {M}ethoden zur {G}ewinnung von a priori-{S}chranken f\"ur harmonische {A}bbildungen }, Journal = { Manuscripta Math. }, Volume = { 40 }, Pages = { 27-77 }, Year = { 1982 } } @Incollection{ JosKar84, Author = { J. Jost and H. Karcher }, Title = { {A}lmost linear functions and a priori estimates for harmonic maps }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 148-155 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Article{ JosLiJPen, Author = { J. Jost and X.Q. Li-Jost and X.W. Peng }, Title = { {C}orrection to "{B}ifurcation of minimal surfaces in {R}iemannian manifolds" }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Note = { (to appear) } } @Article{ JosLiJPen95, Author = { J. Jost and X.Q. Li-Jost and X.W. Peng }, Title = { {B}ifurcation of minimal surfaces in {R}iemannian manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 347 }, Pages = { 51-62 }, Year = { 1995 } } @Article{ JosMei83, Author = { J. Jost and M. Meier }, Title = { {B}oundary regularity for minima of certain quadratic functionals }, Journal = { Math.\ Ann. }, Volume = { 262 }, Pages = { 549-561 }, Year = { 1983 } } @Unpublished{ JosPen, Author = { J. Jost and X.W. Peng }, Title = { {T}he geometry of moduli spaces of stable vector bundles over {R}iemann surfaces }, Note = { SFB237 Bochum } } @Unpublished{ JosPenA, Author = { J. Jost and X.W. Peng }, Title = { {G}roup actions, gauge transformations and the calculus of variations }, Note = { SFB237 Bochum } } @Article{ JosSch82, Author = { J. Jost and R. Schoen }, Title = { {O}n the existence of harmonic diffeomorphisms between surfaces }, Journal = { Invent.\ Math. }, Volume = { 66 }, Pages = { 353-359 }, Year = { 1982 } } @Article{ JosStr90, Author = { J. Jost and M. Struwe }, Title = { {M}orse--{C}onley theory for minimal surfaces of varying topological type }, Journal = { Invent.\ Math. }, Volume = { 102 }, Pages = { 465-499 }, Year = { 1990 } } @Article{ JosXu, Author = { J. Jost and C.J. Xu }, Title = { {S}ubelliptic harmonic maps }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Note = { (to appear) } } @Article{ JosYau83, Author = { J. Jost and S.T. Yau }, Title = { {H}armonic mappings and {K}\"ahler manifolds }, Journal = { Math.\ Ann. }, Volume = { 262 }, Pages = { 145-166 }, Year = { 1983 } } @Article{ JosYau85, Author = { J. Jost and S.T. Yau }, Title = { {A} strong rigidity theorem for a certain class of compact complex analytic surfaces }, Journal = { Math.\ Ann. }, Volume = { 271 }, Pages = { 143-152 }, Year = { 1985 } } @Article{ JosYau86, Author = { J. Jost and S.T. Yau }, Title = { {T}he strong rigidity of locally symmetric complex manifolds of rank one and finite volume }, Journal = { Math.\ Ann. }, Volume = { 275 }, Pages = { 291-304 }, Year = { 1986 } } @Article{ JosYau87, Author = { J. Jost and S.T. Yau }, Title = { {O}n the rigidity of certain discrete groups and algebraic varieties }, Journal = { Math.\ Ann. }, Volume = { 278 }, Pages = { 481-496 }, Year = { 1987 } } @Incollection{ JosYau91, Author = { J. Jost and S.T. Yau }, Title = { {H}armonic maps and group representations }, Booktitle = { {D}ifferential {G}eometry }, Publisher = { Longman Sci. }, Address = { Harlow }, Volume = { 52 }, Pages = { 241-260 }, Series = { Pitman Monographs Surveys Pure Appl.\ Math. }, Year = { 1991 } } @Incollection{ JosYau91A, Author = { J. Jost and S.T. Yau }, Title = { {H}armonic maps and {K}\"ahler geometry }, Booktitle = { {P}rospects in complex geometry. {K}atata {S}ymp. (1989) }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1468 }, Pages = { 340-370 }, Series = { Lecture Notes in Math. }, Year = { 1991 } } @Incollection{ JosYau93, Author = { J. Jost and S.T. Yau }, Title = { {A}pplications of quasilinear {P}{D}{E} to algebraic geometry and arithmetic lattices }, Booktitle = { {A}lgebraic geometry and related topics ({I}nchon, 1992) }, Publisher = { Internat.\ Press }, Address = { Cambridge, MA }, Volume = { 1 }, Pages = { 169-193 }, Series = { Conf.\ Proc.\ Lecture Notes Algebraic Geom. }, Year = { 1993 } } @Article{ JosYau93A, Author = { J. Jost and S.T. Yau }, Title = { {H}armonic mappings and algebraic varieties over function fields }, Journal = { Amer.\ J. Math. }, Volume = { 115 }, Pages = { 1197-1227 }, Year = { 1993 } } @Incollection{ JosYau93B, Author = { J. Jost and S.T. Yau }, Title = { {H}armonic maps and superrigidity }, Booktitle = { {D}ifferential {G}eometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 54 }, Pages = { 245-280 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1993 } } @Article{ JosYau93C, Author = { J. Jost and S.T. Yau }, Title = { {A} nonlinear elliptic system for maps from {H}ermitian to {R}iemannian manifolds and rigidity theorems in {H}ermitian geometry }, Journal = { Acta Math. }, Volume = { 170 }, Pages = { 221-254 }, Year = { 1993 } } @Article{ JosYau94, Author = { J. Jost and S.T. Yau }, Title = { {A} nonlinear elliptic system for maps from {H}ermitian to {R}iemannian manifolds and rigidity theorems in {H}ermitian geometry (correction) }, Journal = { Acta Math. }, Volume = { 173 }, Pages = { 307 }, Year = { 1994 } } @Misc{ JosZuo, Author = { J. Jost and K. Zuo }, Title = { {H}armonic maps into {T}its buildings and factorization of non rigid arithmetic representations of {$\{P}i_1$} of algebraic varieties } } @Unpublished{ JosZuoA, Author = { J. Jost and K. Zuo }, Title = { {H}armonic maps of infinite energy and rigidity results for archimedean and nonarchimedean representations of fundamental groups of quasiprojective varieties }, Note = { preprint } } @Article{ JosZuo94, Author = { J. Jost and K. Zuo }, Title = { {H}armonic maps of infinite energy and rigidity results for quasiprojective varieties }, Journal = { Math.\ Res.\ Lett. }, Volume = { 1 }, Pages = { 631-638 }, Year = { 1994 } } @Article{ JosZuo96, Author = { J. Jost and K. Zuo }, Title = { {H}armonic maps and {${S}l(r,{\bf {C}})$}-representations of fundamental groups of quasiprojective manifolds }, Journal = { J. Algebraic Geom. }, Volume = { 5 }, Pages = { 77-106 }, Year = { 1996 } } @Article{ Jun92, Author = { S.H. Jun }, Title = { {C}urvature estimates for minimal surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 114 }, Pages = { 527-533 }, Year = { 1992 } } @Article{ Jag70, Author = { W. J{\"a}ger }, Title = { {B}ehaviour of minimal surfaces with free boundaries }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 23 }, Pages = { 803-818 }, Year = { 1970 } } @Article{ JagKau79, Author = { W. J{\"a}ger and H. Kaul }, Title = { {U}niqueness and stability of harmonic maps, and their {J}acobi fields }, Journal = { Manuscripta Math. }, Volume = { 28 }, Pages = { 269-291 }, Year = { 1979 } } @Article{ JagKau79A, Author = { W. J{\"a}ger and H. Kaul }, Title = { {U}niqueness of harmonic mappings and of solutions of elliptic equations on {R}iemannian manifolds }, Journal = { Math.\ Ann. }, Volume = { 240 }, Pages = { 231-250 }, Year = { 1979 } } @Article{ JagKau83, Author = { W. J{\"a}ger and H. Kaul }, Title = { {R}otationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems }, Journal = { J. Reine Angew.\ Math. }, Volume = { 343 }, Pages = { 146-161 }, Year = { 1983 } } @Article{ Jor55, Author = { K. J{\"o}rgens }, Title = { {H}armonische {A}bbildungen und die {D}ifferentialgleichung {$rt-s^2 = 1$} }, Journal = { Math.\ Ann. }, Volume = { 129 }, Pages = { 330-344 }, Year = { 1955 } } @Incollection{ KDuSIaAMP94, Author = { K.Duggal and S.Ianus and A.M.Pastore }, Title = { {H}armonic maps on {$f$}-manifold with semi-{R}iemannian metrics }, Booktitle = { {P}roceedings of the {C}onference on {G}eometry and {T}opology, {S}ept.26-29, 1993, {C}luj-{N}apoca {U}niv., {R}omania }, Pages = { 47-55 }, Year = { 1994 } } @Article{ Kal80, Author = { M. Kalka }, Title = { {D}eformation of submanifolds of strongly negatively curved manifolds }, Journal = { Math.\ Ann. }, Volume = { 251 }, Pages = { 243-248 }, Year = { 1980 } } @Incollection{ Kal82, Author = { M. Kalka }, Title = { {H}armonic maps in {K}\"ahler geometry and deformation theory }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 75-86 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Unpublished{ KamRuhTon, Author = { F.W. Kamber and E.A. Ruh and P. Tondeur }, Title = { {C}omparing {R}iemannian foliations with transversally symmetric foliations }, Note = { Preprint } } @Incollection{ KamRuhTon86, Author = { F.W. Kamber and E.A. Ruh and P. Tondeur }, Title = { {A}lmost transversally symmetric foliations }, Booktitle = { {D}ifferential {G}eometry, {P}e\~niscola 1985 }, Editor = { A.M. Naveira and A. Ferr{\'a}ndez and F. Mascar{\'o} }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1209 }, Pages = { 184-189 }, Series = { Lecture Notes in Math. }, Year = { 1986 } } @Misc{ KamTon, Author = { F.W. Kamber and P. Tondeur }, Title = { {T}he second variation formula for harmonic foliations } } @Article{ KamTon80, Author = { F.W. Kamber and P. Tondeur }, Title = { {F}euilletages harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 291 }, Pages = { 409-411 }, Year = { 1980 } } @Article{ KamTon82, Author = { F.W. Kamber and P. Tondeur }, Title = { {D}ualit\'e de {P}oincar\'e pour les feuilletages harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 294 }, Pages = { 357-359 }, Year = { 1982 } } @Incollection{ KamTon82A, Author = { F.W. Kamber and P. Tondeur }, Title = { {H}armonic foliations }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 87-121 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ KamTon82B, Author = { F.W. Kamber and P. Tondeur }, Title = { {I}nfinitesimal automorphisms and second variation of the energy for harmonic foliations }, Journal = { T\^ohoku Math.\ J. }, Volume = { 34 }, Pages = { 525-538 }, Year = { 1982 } } @Incollection{ KamTon83, Author = { F.W. Kamber and P. Tondeur }, Title = { {D}uality for {R}iemannian foliations }, Booktitle = { {S}ingularities }, Editor = { P. Orlik }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 40 }, Pages = { 609-618 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1983 } } @Incollection{ KamTon83A, Author = { F.W. Kamber and P. Tondeur }, Title = { {F}oliations and metrics }, Booktitle = { {P}roc. of the 1981-82 year in differential geometry, {U}niversity of {M}aryland }, Publisher = { Birkh\"auser }, Volume = { 32 }, Pages = { 103-152 }, Series = { Progr.\ Math. }, Year = { 1983 } } @Article{ KamTon83B, Author = { F.W. Kamber and P. Tondeur }, Title = { {T}he index of harmonic foliations on spheres }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 275 }, Pages = { 257-263 }, Year = { 1983 } } @Article{ KamTon84, Author = { F.W. Kamber and P. Tondeur }, Title = { {C}urvature properties of harmonic foliations }, Journal = { Illinois J. Math. }, Volume = { 28 }, Pages = { 458-471 }, Year = { 1984 } } @Article{ KamTon84A, Author = { F.W. Kamber and P. Tondeur }, Title = { {D}uality theorems for foliations }, Journal = { Ast{\'e}risque }, Volume = { 116 }, Pages = { 108-116 }, Year = { 1984 } } @Incollection{ KamTon85, Author = { F.W. Kamber and P. Tondeur }, Title = { {T}he {B}ernstein problem for foliations }, Booktitle = { {G}lobal differential geometry and global analysis 1984 }, Editor = { D. Ferus and R.B. Gardner and S. Helgason and U. Simon }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1156 }, Pages = { 216-218 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Article{ KamTonTot87, Author = { F.W. Kamber and P. Tondeur and G. Toth }, Title = { {T}ransversal {J}acobi fields for harmonic foliations }, Journal = { Michigan Math.\ J. }, Volume = { 34 }, Pages = { 261-266 }, Year = { 1987 } } @Article{ KanPak96, Author = { T.H. Kang and J.S. Pak }, Title = { {O}n the spectal geometry for the {J}acobi operators of harmonic maps into a quaternionic projective space }, Journal = { Geom.\ Dedicata }, Volume = { 60 }, Pages = { 153-161 }, Year = { 1996 } } @Article{ Kap87, Author = { N. Kapouleas }, Title = { {C}onstant mean curvature surfaces in {E}uclidean three-space }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 17 }, Pages = { 318-320 }, Year = { 1987 } } @Article{ Kap90, Author = { N. Kapouleas }, Title = { {C}omplete constant mean curvature surfaces in {E}uclidean three-space }, Journal = { Ann.\ of Math. }, Volume = { 131 }, Pages = { 239-330 }, Year = { 1990 } } @Article{ Kap91, Author = { N. Kapouleas }, Title = { {C}ompact constant mean curvature surfaces in {E}uclidean three-space }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 683-715 }, Year = { 1991 } } @Article{ Kap95, Author = { N. Kapouleas }, Title = { {C}onstant mean curvature surfaces constructed by fusing {W}ente tori }, Journal = { Invent.\ Math. }, Volume = { 119 }, Pages = { 443-518 }, Year = { 1995 } } @Misc{ Kar, Author = { H. Karcher }, Title = { {F}amilies of triply-periodic surfaces of constant mean curvature } } @Misc{ KarA, Author = { H. Karcher }, Title = { {N}ew examples of periodic minimal surfaces } } @Article{ Kar88, Author = { H. Karcher }, Title = { {E}mbedded minimal surfaces derived from {S}cherk's examples }, Journal = { Manuscripta Math. }, Volume = { 62 }, Pages = { 83-114 }, Year = { 1988 } } @Unpublished{ Kar89, Author = { H. Karcher }, Title = { {C}onstruction of minimal surfaces }, Note = { Vorles. 12 Bonn }, Year = { 1989 } } @Article{ Kar89A, Author = { H. Karcher }, Title = { {T}he triply-periodic minimal surfaces of {A}lan {S}choen and their constant mean curvature companions }, Journal = { Manuscripta Math. }, Volume = { 64 }, Pages = { 291-357 }, Year = { 1989 } } @Article{ KarPinSte88, Author = { H. Karcher and U. Pinkall and I. Sterling }, Title = { {N}ew minimal surfaces in {${S}^3$} }, Journal = { J. Differential Geom. }, Volume = { 28 }, Pages = { 169-185 }, Year = { 1988 } } @Article{ KarWoo84, Author = { H. Karcher and J.C. Wood }, Title = { {N}on-existence results and growth properties for harmonic maps and forms }, Journal = { J. Reine Angew.\ Math. }, Volume = { 353 }, Pages = { 165-180 }, Year = { 1984 } } @Article{ Kar81, Author = { L. Karp }, Title = { {O}n {S}tokes' theorem for noncompact manifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 82 }, Pages = { 487-490 }, Year = { 1981 } } @Incollection{ Kar82, Author = { L. Karp }, Title = { {S}ubharmonic functions, harmonic mappings, and isometric immersions }, Booktitle = { {S}eminar on {D}ifferential {G}eometry }, Editor = { S.T. Yau }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 102 }, Pages = { 133-142 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1982 } } @Article{ Kar82A, Author = { L. Karp }, Title = { {S}ubharmonic functions on real and complex manifolds }, Journal = { Math.\ Z. }, Volume = { 179 }, Pages = { 535-554 }, Year = { 1982 } } @Incollection{ Kar83, Author = { L. Karp }, Title = { {T}he growth of harmonic functions and mappings }, Booktitle = { {D}iff. {G}eo. {P}roc. {S}pecial {Y}ear 1981-2. {M}aryland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 32 }, Pages = { 153-161 }, Series = { Progr.\ Math. }, Year = { 1983 } } @Article{ Kar85, Author = { L. Karp }, Title = { {D}ifferential inequalities on complete {R}iemannian manifolds and applications }, Journal = { Math.\ Ann. }, Volume = { 272 }, Pages = { 449-459 }, Year = { 1985 } } @Unpublished{ Kas, Author = { A. Kasue }, Title = { {M}easured {H}ausdorff convergence of {R}iemannian manifolds }, Note = { preprint } } @Article{ Kas81, Author = { A. Kasue }, Title = { {O}n {R}iemannian manifolds admitting certain convex functions }, Journal = { Osaka J. Math. }, Volume = { 18 }, Pages = { 577-582 }, Year = { 1981 } } @Incollection{ Kas84, Author = { A. Kasue }, Title = { {E}stimates for solutions of {P}oisson equation and their applications to submanifolds }, Booktitle = { {D}ifferential geometry of submanifolds }, Editor = { K. Kenmotsu }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1090 }, Pages = { 1-14 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ Kas86, Author = { A. Kasue }, Title = { {G}ap theorems for minimal submanifolds of {E}uclidean space }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 38 }, Pages = { 473-492 }, Year = { 1986 } } @Article{ Kas88, Author = { A. Kasue }, Title = { {A} compactification of a manifold with asymptotically nonnegative curvature }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 21 }, Pages = { 593-622 }, Year = { 1988 } } @Incollection{ Kas88A, Author = { A. Kasue }, Title = { {H}armonic functions with growth conditions on a manifold with asymptotically nonnegative curvature {I} }, Booktitle = { {G}eometry and analysis on manifolds }, Editor = { T. Sunada }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1339 }, Pages = { 158-181 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Article{ Kas90, Author = { A. Kasue }, Title = { {H}armonic functions with growth conditions on a manifold with asymptotically nonnegative curvature {I}{I} }, Journal = { Adv.\ Stud.\ Pure Math. }, Volume = { 18-I }, Pages = { 283-301 }, Year = { 1990 } } @Incollection{ Kas93, Author = { A. Kasue }, Title = { {H}armonic functions of polynomial growth on complete manifold }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 281-290 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ KasWas90, Author = { A. Kasue and T. Washio }, Title = { {G}rowth of equivariant harmonic maps and harmonic morphisms }, Journal = { Osaka J. Math. }, Volume = { 27 }, Pages = { 899-928 }, Year = { 1990 } } @Article{ KasWas92, Author = { A. Kasue and T. Washio }, Title = { {E}rrata to {G}rowth of equivariant harmonic maps and harmonic morphisms }, Journal = { Osaka J. Math. }, Volume = { 29 }, Pages = { 419-420 }, Year = { 1992 } } @Article{ Kat62, Author = { Y. Katsurada }, Title = { {G}eneralized {M}inkowski formulas for closed hypersurfaces in {R}iemann space }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 57 }, Pages = { 283-293 }, Year = { 1962 } } @Article{ Kau71, Author = { H. Kaul }, Title = { {E}in {E}inschlossungssatz f\"ur {${H}$}-{F}l\"achen in {R}iemannschen {M}annigfaltigkeiten }, Journal = { Manuscripta Math. }, Volume = { 5 }, Pages = { 103-112 }, Year = { 1971 } } @Article{ Kau74, Author = { H. Kaul }, Title = { {O}n minimal surfaces in a {R}iemannian manifold }, Journal = { Math.\ J. Okayama Univ. }, Volume = { 32 }, Pages = { 19-38 }, Year = { 1974 } } @Article{ Kau77, Author = { H. Kaul }, Title = { {D}er {D}irichletproblem f\"ur elliptische {D}ifferentialoperatoren mit {V}ariationsstruktur auf {R}iemannschen {M}annigfaltigkeiten }, Journal = { Bonn.\ Math.\ Schriften }, Volume = { 94 }, Year = { 1977 } } @Article{ Kaw82, Author = { S. Kawai }, Title = { {O}n the instability of a minimal surface in a {$4$}-manifold whose curvature lies in the interval {$(1/4,1]$} }, Journal = { Publ.\ Res.\ Inst.\ Math.\ Sci. }, Volume = { 18 }, Pages = { 1067-1075 }, Year = { 1982 } } @Article{ Kaw84, Author = { S. Kawai }, Title = { {A} theorem of {B}ernstein type for minimal surfaces in {${\bf {R}}^4$} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 36 }, Pages = { 377-384 }, Year = { 1984 } } @Misc{ KawNakTak, Author = { S. Kawai and N. Nakauchi and H. Takeuchi }, Title = { {A} remark on the existence of {$n$}-harmonic spheres } } @Incollection{ Kaw91, Author = { B. Kawohl }, Title = { {F}rom {$p$}-{L}aplace to mean curvature operator and related questions }, Booktitle = { {P}rogress in {P}artial {D}ifferential {E}quations: the {M}etz surveys }, Publisher = { Longman }, Address = { Harlow }, Volume = { 249 }, Pages = { 40-56 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1991 } } @Incollection{ Kaz83, Author = { J.L. Kazdan }, Title = { {S}ome applications of partial differential equations to problems in geometry }, Booktitle = { {S}urveys in {G}eometry }, Series = { University of Tokyo Lecture Notes }, Year = { 1983 } } @Article{ Kaz88, Author = { J.L. Kazdan }, Title = { {U}nique continuation in geometry }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 41 }, Pages = { 667-681 }, Year = { 1988 } } @Article{ KelSil88, Author = { G. Keller and R. Silvotti }, Title = { {Q}uantum measure and {W}eyl anomaly of two-dimensional bosonic nonlinear {$\sigma$}-models }, Journal = { Ann.\ Physics }, Volume = { 183 }, Pages = { 269-308 }, Year = { 1988 } } @Article{ KelRubSte89, Author = { J.B. Keller and J. Rubenstein and P. Sternberg }, Title = { {R}eaction-diffusion processes and evolution to harmonic maps }, Journal = { SIAM J. Appl.\ Math. }, Volume = { 49 }, Pages = { 1722-1733 }, Year = { 1989 } } @Misc{ KelRubSte, Author = { J. Keller and J. Rubenstein and P. Sternberg }, Title = { {R}eaction-diffusion processes and evolution of harmonic maps } } @Article{ Kel73, Author = { E. Kelly }, Title = { {C}ohomology of compact minimal submanifolds }, Journal = { Michigan Math.\ J. }, Volume = { 19 }, Pages = { 133-135 }, Year = { 1973 } } @Incollection{ Ken81, Author = { W.S. Kendall }, Title = { {B}rownian motion, negative curvature, and harmonic maps }, Booktitle = { {S}tochastic {I}ntegrals }, Editor = { D. Williams }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 851 }, Pages = { 479-491 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Article{ Ken83, Author = { W.S. Kendall }, Title = { {B}rownian motion and a generalized little {P}icard theorem }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 275 }, Pages = { 751-760 }, Year = { 1983 } } @Article{ Ken86, Author = { W.S. Kendall }, Title = { {N}onnegative {R}icci curvature and the {B}rownian coupling property }, Journal = { Stochastics }, Volume = { 19 }, Pages = { 111-129 }, Year = { 1986 } } @Article{ Ken86A, Author = { W.S. Kendall }, Title = { {S}tochastic differential geometry, a coupling property, and harmonic maps }, Journal = { J. London Math.\ Soc. }, Volume = { 33 }, Pages = { 554-566 }, Year = { 1986 } } @Article{ Ken87, Author = { W.S. Kendall }, Title = { {S}tochastic differential geometry: {A}n introduction }, Journal = { Acta Appl.\ Math. }, Volume = { 9 }, Pages = { 29-60 }, Year = { 1987 } } @Incollection{ Ken88, Author = { W.S. Kendall }, Title = { {M}artingales on manifolds and harmonic maps }, Booktitle = { {G}eometry of random motion }, Editor = { R. Durrett and M.A. Pinsky }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 73 }, Pages = { 121-157 }, Note = { (See H. Huang and W.S. Kendall for correction) }, Series = { Contemp.\ Math. }, Year = { 1988 } } @Article{ Ken90, Author = { W.S. Kendall }, Title = { {P}robability, convexity and harmonic maps with small image {I}: uniqueness and fine existence }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 61 }, Pages = { 371-406 }, Year = { 1990 } } @Article{ Ken91, Author = { W.S. Kendall }, Title = { {C}onvexity and the hemisphere }, Journal = { J. London Math.\ Soc. }, Volume = { 43 }, Pages = { 567-576 }, Year = { 1991 } } @Incollection{ Ken93, Author = { W.S. Kendall }, Title = { {B}rownian motion and partial differential equations: from the heat equation to harmonic maps }, Booktitle = { {P}roc. {I}{S}{I} 49th session }, Address = { Firenze }, Pages = { 85-101 }, Year = { 1993 } } @Article{ Ken94, Author = { W.S. Kendall }, Title = { {P}robability, convexity and harmonic maps {I}{I}: smoothness via probabilistic gradient inequalities }, Journal = { J. Funct.\ Anal. }, Volume = { 126 }, Pages = { 228-257 }, Year = { 1994 } } @Misc{ Ken, Author = { K. Kenmotsu }, Title = { {T}he classification of minimal surfaces with constant {G}aussian curvature in a space form } } @Article{ Ken75, Author = { K. Kenmotsu }, Title = { {O}n a paramatrization of minimal immersions of {${\bf {R}}^2$} into {${S}^5$} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 27 }, Pages = { 83-90 }, Year = { 1975 } } @Article{ Ken76, Author = { K. Kenmotsu }, Title = { {O}n minimal immersions of {${\bf {R}}^2$} into {${S}^n$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 28 }, Pages = { 182-191 }, Year = { 1976 } } @Article{ Ken79, Author = { K. Kenmotsu }, Title = { {W}eierstrass formula for surfaces of prescribed mean curvature }, Journal = { Math.\ Ann. }, Volume = { 245 }, Pages = { 89-99 }, Year = { 1979 } } @Article{ Ken80, Author = { K. Kenmotsu }, Title = { {S}urfaces of revolution with prescribed mean curvature }, Journal = { T\^ohoku Math.\ J. }, Volume = { 32 }, Pages = { 147-153 }, Year = { 1980 } } @Article{ Ken83A, Author = { K. Kenmotsu }, Title = { {M}inimal surfaces with constant curvature in {$4$}-dimensional space forms }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 89 }, Pages = { 133-138 }, Year = { 1983 } } @Incollection{ Ken84, Author = { K. Kenmotsu }, Title = { {G}auss maps of surfaces with constant mean curvature }, Booktitle = { {D}ifferential {G}eometry of {S}ubmanifolds }, Editor = { K. Kenmotsu }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1090 }, Pages = { 129-132 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ Ken85, Author = { K. Kenmotsu }, Title = { {O}n minimal immersions of {${\bf {R}}^2$} into {${P}^n({\bf {C}})$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 37 }, Pages = { 665-682 }, Year = { 1985 } } @Article{ Ken87A, Author = { K. Kenmotsu }, Title = { {T}he mean curvature vector of surfaces in {${\bf {R}}^4$} }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 19 }, Pages = { 458-462 }, Year = { 1987 } } @Incollection{ Ken93A, Author = { K. Kenmotsu }, Title = { {M}inimal surfaces of constant curvature in complex projective spaces }, Booktitle = { {G}eo. and its {A}ppl. }, Publisher = { World Sci. }, Pages = { 85-92 }, Year = { 1993 } } @Article{ Ken94A, Author = { K. Kenmotsu }, Title = { {A}n intrinsic characterization of {H}-deformable surfaces }, Journal = { J. London Math.\ Soc. }, Volume = { 49 }, Pages = { 555-568 }, Year = { 1994 } } @Article{ KerMar84, Author = { P. Kersten and R. Martini }, Title = { {T}he harmonic map and {K}illing fields for self-dual {${S}{U}(3)$} {Y}ang--{M}ills equations }, Journal = { J. Phys.\ A }, Volume = { 17 }, Pages = { L227-230 }, Year = { 1984 } } @Article{ Kik81, Author = { N. Kikuchi }, Title = { {O}n the nonlinear parabolic equation of {E}ells--{S}ampson and a harmonic mapping with boundary condition }, Journal = { Keio Math.\ Sem.\ Report }, Volume = { 6 }, Pages = { 33-40 }, Year = { 1981 } } @Article{ Kil85, Author = { T.P. Killingback }, Title = { {N}onlinear {$\sigma$}-models on compact {R}iemann surfaces }, Journal = { Analysis }, Volume = { 5 }, Pages = { 251-274 }, Year = { 1985 } } @Article{ Kil85A, Author = { T.P. Killingback }, Title = { {N}onlinear {$\sigma$}-models on compact {R}iemann surfaces }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 100 }, Pages = { 481-494 }, Year = { 1985 } } @Article{ KimYim96, Author = { Y.H. Kim and J,W. Yim }, Title = { {H}armonic maps into open manifolds with nonnegative curvature }, Journal = { Comm.\ Korean Math.\ Soc. }, Volume = { 11 }, Pages = { 789--796 }, Year = { 1996 } } @Article{ Kir86, Author = { F. Kirwan }, Title = { {O}n spaces of maps from {R}iemann surfaces to {G}rassmannians and applications to the cohomology of moduli of vector bundles }, Journal = { Ark.\ Mat. }, Volume = { 24 }, Pages = { 221-275 }, Year = { 1986 } } @Article{ Kis88, Author = { T. Kiss-T{\'o}th }, Title = { {E}xact solutions of nonlinear {${S}{U}({N})$} principal {$\sigma$}-models }, Journal = { Internat.\ J. Modern Phys.\ A }, Volume = { 3 }, Pages = { 665-702 }, Year = { 1988 } } @Book{ Kli78, Author = { W. Klingenberg }, Title = { {L}ectures on closed geodesics }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 230 }, Series = { Grundlehren Math.\ Wiss. }, Year = { 1978 } } @Article{ Klo67, Author = { T. Klotz }, Title = { {S}urfaces harmonically immersed in {${E}^3$} }, Journal = { Pacific J. Math. }, Volume = { 21 }, Pages = { 79-87 }, Year = { 1967 } } @Article{ KloOss67, Author = { T. Klotz and R. Osserman }, Title = { {C}omplete surfaces in {${E}^3$} with constant mean curvature }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 41 }, Pages = { 313-318 }, Year = { 1966/67 } } @Article{ KloSar66, Author = { T. Klotz and L. Sario }, Title = { {G}auss mapping of arbitrary minimal surfaces }, Journal = { J. Analyse Math. }, Volume = { 17 }, Pages = { 209-217 }, Year = { 1966 } } @Article{ Kne30, Author = { H. Kneser }, Title = { {D}ie kleinste {B}edeckungszahl innerhalb einer {K}lasse von {F}l\"achenabbildungen }, Journal = { Math.\ Ann. }, Volume = { 103 }, Pages = { 347-358 }, Year = { 1930 } } @Article{ KniStoWhi85, Author = { R.J. Knill and W.R. Stoeger and A.P. Whitman }, Title = { {T}he harmonic mapping character of {R}osen's bi-metric theory of gravity and the geometry of its harmonic mapping space }, Journal = { J. Math.\ Phys. }, Volume = { 26 }, Pages = { 2032-2038 }, Year = { 1985 } } @Incollection{ KniStoWhi86, Author = { R.J. Knill and W.R. Stoeger and A.P. Whitman }, Title = { {T}he decomposition and superposition of rank-one gravitational potential tensors }, Booktitle = { {N}onlinear problems in geometry }, Editor = { D. DeTurck }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 51 }, Pages = { 81-91 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Article{ KniStoWhi86A, Author = { R.J. Knill and W.R. Stoeger and A.P. Whitman }, Title = { {S}ome harmonic maps on pseudo-{R}iemannian manifolds }, Journal = { Internat.\ J. Theoret.\ Phys. }, Volume = { 25 }, Pages = { 1139-1153 }, Year = { 1986 } } @Article{ Kno80, Author = { H. Kn{\"o}rrer }, Title = { {G}eodesics on the ellipsoid }, Journal = { Invent.\ Math. }, Volume = { 59 }, Pages = { 119-143 }, Year = { 1980 } } @Article{ Kno82, Author = { H. Kn{\"o}rrer }, Title = { {G}eodesics on quadrics and a mechanical problem of {C}. {N}eumann }, Journal = { J. Reine Angew.\ Math. }, Volume = { 334 }, Pages = { 69-78 }, Year = { 1982 } } @Article{ Kno86, Author = { H. Kn{\"o}rrer }, Title = { {I}ntegrable {H}amiltonsche {S}ysteme und algebraische {G}eometrie }, Journal = { J. Deutsch.\ Math.\ Verein. }, Volume = { 88 }, Pages = { 82-103 }, Year = { 1986 } } @Unpublished{ Kob93, Author = { P.Z. Kobak }, Title = { {Q}uaternionic geometry and harmonic maps }, Note = { Oxford D. Phil. thesis }, Year = { 1993 } } @Article{ Kob94, Author = { P.Z. Kobak }, Title = { {B}irational correspondences between twistor spaces }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 26 }, Pages = { 186-190 }, Year = { 1994 } } @Incollection{ Kob94A, Author = { P.Z. Kobak }, Title = { {T}wistors, nilpotent orbits and harmonic maps }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 295-319 }, Series = { Aspects of Math. }, Year = { 1994 } } @Unpublished{ KobLoo96, Author = { P.Z. Kobak and B. Loo }, Title = { {M}oduli of quaternionic superminimal immersions of {$2$}-spheres into quaternionic projective spaces }, Note = { Preprint }, Year = { 1996 } } @Article{ KobSwa93, Author = { P.Z. Kobak and A. Swann }, Title = { {Q}uaternionic geometry of the nilpotent variety }, Journal = { Math.\ Ann. }, Volume = { 297 }, Pages = { 747-764 }, Year = { 1993 } } @Incollection{ Kob61, Author = { S. Kobayashi }, Title = { {C}anonical forms on frame bundles of higher order contact }, Booktitle = { {D}ifferential {G}eometry }, Editor = { C.B. Allendoefer }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 3 }, Pages = { 186-193 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1961 } } @Book{ Kob70, Author = { S. Kobayashi }, Title = { {H}yperbolic manifolds and holomorphic mappings }, Publisher = { Dekker }, Address = { New York }, Year = { 1970 } } @Article{ Kob76, Author = { S. Kobayashi }, Title = { {I}ntrinsic distances, measures and geometric function theory }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 82 }, Pages = { 357-416 }, Year = { 1976 } } @Article{ Kob78, Author = { S. Kobayashi }, Title = { {C}omplex manifolds with nonpositive holomorphic sectional curvature and hyperbolicity }, Journal = { T\^ohoku Math.\ J. }, Volume = { 30 }, Pages = { 487-489 }, Year = { 1978 } } @Article{ KobWu70, Author = { S. Kobayashi and H.H. Wu }, Title = { {O}n holomorphic sections of certain {H}ermitian vector bundles }, Journal = { Math.\ Ann. }, Volume = { 189 }, Pages = { 1-4 }, Year = { 1970 } } @Article{ KobYan66, Author = { S. Kobayashi and K. Yano }, Title = { {P}rolongations of tensor fields and connections to tangent bundles {I}: general theory }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 18 }, Pages = { 195-210 }, Year = { 1966 } } @Misc{ Koh, Author = { S.E. Koh }, Title = { {A} {L}iouville type theorem for harmonic maps } } @Article{ Koh91, Author = { S.E. Koh }, Title = { {A}nother nonexistence theorem for stable harmonic maps }, Journal = { Hak-sul Chi }, Volume = { 35 }, Pages = { 19-25 }, Year = { 1991 } } @Article{ Koh93, Author = { S.E. Koh }, Title = { {T}he stability of complete noncompact surfaces with constant mean curvature }, Journal = { Math.\ J. Toyama Univ. }, Volume = { 16 }, Pages = { 15-17 }, Year = { 1993 } } @Article{ KohRos65, Author = { J.J. Kohn and H. Rossi }, Title = { {O}n the extension of holomorphic functions from the boundary of a complex manifold }, Journal = { Ann.\ of Math. }, Volume = { 81 }, Pages = { 451-472 }, Year = { 1965 } } @Misc{ Koi, Author = { M. Koiso }, Title = { {S}tability of surfaces with constant mean curvature in {${\bf {R}}^3$} } } @Article{ Koi86, Author = { M. Koiso }, Title = { {T}he uniqueness for minimal surfaces in {${S}^3$} }, Journal = { Manuscripta Math. }, Pages = { 193-207 }, Year = { 1986 } } @Incollection{ Koi93, Author = { M. Koiso }, Title = { {A} uniqueness result for minimal surfaces in {${S}^3$} }, Booktitle = { {P}rogress in {D}ifferential {G}eometry }, Publisher = { Kinokuniya }, Address = { Tokyo }, Volume = { 22 }, Pages = { 117-122 }, Series = { Adv.\ Stud.\ Pure Math. }, Year = { 1993 } } @Article{ Koi79, Author = { N. Koiso }, Title = { {V}ariation of harmonic mappings caused by a deformation of {R}iemannian metrics }, Journal = { Hokkaido Math.\ J. }, Volume = { 8 }, Pages = { 199-213 }, Year = { 1979 } } @Article{ Koi83, Author = { N. Koiso }, Title = { {O}n the space of minimal surfaces with boundaries }, Journal = { Osaka J. Math. }, Volume = { 20 }, Pages = { 911-921 }, Year = { 1983 } } @Article{ Koi84, Author = { N. Koiso }, Title = { {O}n the stability of minimal surfaces in {${\bf {R}}^3$} }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 36 }, Pages = { 523-541 }, Year = { 1984 } } @Incollection{ Koi84A, Author = { N. Koiso }, Title = { {T}he stability and the {G}auss map of minimal surfaces in {${\bf {R}}^3$} }, Booktitle = { {D}ifferential {G}eometry of {S}ubmanifolds }, Editor = { K. Kenmotsu }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1090 }, Pages = { 77-92 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ Koi92, Author = { N. Koiso }, Title = { {E}lasticae in a {R}iemannian manifold }, Journal = { Osaka J. Math. }, Volume = { 29 }, Pages = { 539-543 }, Year = { 1992 } } @Article{ Kon90, Author = { J.J. Konderak }, Title = { {C}onstruction of harmonic maps between pseudo-{R}iemannian spheres and hyperbolic spaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 109 }, Pages = { 469-476 }, Year = { 1990 } } @Article{ Kon91, Author = { J.J. Konderak }, Title = { {H}urwitz theorem for seminormal algebras }, Journal = { Atti Sem.\ Mat.\ Fis.\ Univ.\ Modena }, Volume = { 39 }, Pages = { 403-411 }, Year = { 1991 } } @Article{ Kon91A, Author = { J.J. Konderak }, Title = { {O}n natural first order {L}agrangians }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 23 }, Pages = { 169-174 }, Year = { 1991 } } @Article{ Kon92, Author = { J.J. Konderak }, Title = { {O}n equivariant harmonic maps between pseudo-{R}iemannian manifolds }, Journal = { Bull.\ Math.\ Soc.\ Sci.\ Math.\ R. S. Roumanie (N.S.) }, Volume = { 36 }, Pages = { 143-145 }, Year = { 1992 } } @Article{ Kon92A, Author = { J.J. Konderak }, Title = { {O}n harmonic vector fields }, Journal = { Publ.\ Mat. }, Volume = { 36 }, Pages = { 217-228 }, Year = { 1992 } } @Incollection{ KondiT89, Author = { J.J. Konderak and L. di~Terlizzi }, Title = { {O}n some construction of harmonic maps between pseudo-{R}iemannian manifolds }, Booktitle = { {D}ifferential {G}eometry and its {A}pplications ({E}ger, 1989) }, Publisher = { North Holland }, Address = { Amsterdam }, Volume = { 56 }, Pages = { 215-222 }, Series = { Colloq.\ Math.\ Soc.\ J\'anos Bolyai }, Year = { 1989 } } @Article{ KorKus93, Author = { N.J. Korevaar and R. Kusner }, Title = { {T}he global structure of constant mean curvature surfaces }, Journal = { Invent.\ Math. }, Volume = { 114 }, Pages = { 311-332 }, Year = { 1993 } } @Incollection{ KorKus93A, Author = { N.J. Korevaar and R. Kusner }, Title = { {T}he structure of constant mean curvature embeddings in {E}uclidean three space }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54 part 1 }, Pages = { 291-297 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ KorKusSol89, Author = { N.J. Korevaar and R. Kusner and B. Solomon }, Title = { {T}he structure of complete embedded surfaces with constant mean curvature }, Journal = { J. Differential Geom. }, Volume = { 30 }, Pages = { 465-503 }, Year = { 1989 } } @Article{ KorLew87, Author = { N.J. Korevaar and J. Lewis }, Title = { {C}onvex solutions to certain elliptic equations having constant rank {H}essians }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 97 }, Pages = { 19-32 }, Year = { 1987 } } @Article{ KorSch93, Author = { N.J. Korevaar and R.M. Schoen }, Title = { {S}obolev spaces and harmonic maps for metric space targets }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 561-659 }, Year = { 1993 } } @Unpublished{ Kor, Author = { D.A. Korotkin }, Title = { {O}n some integrable cases in surface theory }, Note = { Berlin preprint } } @Book{ Kos60, Author = { J.L. Koszul }, Title = { {L}ectures on fibre bundles and differential geometry }, Publisher = { Tata Inst.\ Fund.\ Res. }, Address = { Bombay }, Volume = { 20 }, Series = { Tata Inst.\ Fund.\ Res.\ Lectures on Math.\ and Phys. }, Year = { 1960 } } @Article{ KosMal58, Author = { J.L. Koszul and B. Malgrange }, Title = { {S}ur certaines structures fibr\'ees complexes }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 9 }, Pages = { 102-109 }, Year = { 1958 } } @Article{ Kot94, Author = { M. Kotani }, Title = { {C}onnectedness of the space of minimal {$2$}-spheres in {${S}^n(1)$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 120 }, Pages = { 803-810 }, Year = { 1994 } } @Article{ Kot97, Author = { M. Kotani }, Title = { {H}armonic {$2$}-spheres with {$r$} pairs of extra eigenfunctions }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 125 }, Pages = { 2083--2092 }, Year = { 1997 } } @Article{ Kou83, Author = { T. Koufogiorgos }, Title = { {A} characterization of a minimal submanifold of {${\bf {R}}^{n+p}$} }, Journal = { Ann.\ Polon.\ Math. }, Volume = { 40 }, Pages = { 233-237 }, Year = { 1983 } } @Misc{ Kou, Author = { M. Kourouma }, Title = { {A}bout the regularity of energy minimizing maps with values in a metric space of curvature bounded above } } @Misc{ KouA, Author = { M. Kourouma }, Title = { {H}armonic section of {R}iemannian fiber bundles } } @Incollection{ Kov89, Author = { M. Kovalyov }, Title = { {S}ingularity of harmonic maps on {M}inkowski space }, Booktitle = { {D}ifferential {E}quations and {A}pplications {V}ol. {I}, {I}{I} }, Publisher = { Ohio Univ.\ Press }, Address = { Athens OH }, Pages = { 44-48 }, Year = { 1989 } } @Article{ KozSim84, Author = { M. Kozlowski and U. Simon }, Title = { {M}inimal immersions of {$2$}-manifolds into spheres }, Journal = { Math.\ Z. }, Volume = { 186 }, Pages = { 377-382 }, Year = { 1984 } } @Article{ Kro96, Author = { W. Kr{\'o}likowski }, Title = { {F}ueter regular mappings and harmonicity }, Journal = { Ann.\ Polon.\ Math. }, Volume = { 64 }, Pages = { 97-114 }, Year = { 1996 } } @Article{ Kum95, Author = { H. Kumura }, Title = { {T}he {D}irichlet problem at infinity on {H}adamard manifolds }, Journal = { Nagoya Math.\ J. }, Volume = { 138 }, Pages = { 1-18 }, Year = { 1995 } } @Misc{ Kun, Author = { A. Kundu }, Title = { {C}onstruction of non-linear {$\sigma$}-models in two and higher space dimensions } } @Article{ Kun86, Author = { A. Kundu }, Title = { {G}auge equivalence of {$\sigma$} models with noncompact {G}rassmannian manifolds }, Journal = { J. Phys.\ A }, Volume = { 19 }, Pages = { 1303-1313 }, Year = { 1986 } } @Article{ Kus87, Author = { R. Kusner }, Title = { {C}onformal geometry and complete minimal surfaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 17 }, Pages = { 291-295 }, Year = { 1987 } } @Misc{ KusSch, Author = { R. Kusner and N. Schmitt }, Title = { {T}he spinor representation of minimal surfaces } } @Misc{ Kuw, Author = { E.C. Kuwert }, Title = { {E}mbedded solutions for exterior minimal surface problems } } @Article{ Kuw94, Author = { E.C. Kuwert }, Title = { {M}inimizing the energy of maps from a surface into a {$2$}-sphere with prescribed degree and boundary values }, Journal = { Manuscripta Math. }, Volume = { 83 }, Pages = { 31-38 }, Year = { 1994 } } @Article{ Kuw96, Author = { E.C. Kuwert }, Title = { {H}armonic maps between flat surfaces with conical singularities }, Journal = { Math.\ Z. }, Volume = { 221 }, Pages = { 421-436 }, Year = { 1996 } } @Article{ Kus84, Author = { A. K{\"u}ster }, Title = { {A}n optimal estimate of the free boundary of a minimal surface }, Journal = { J. Reine Angew.\ Math. }, Volume = { 349 }, Pages = { 55-62 }, Year = { 1984 } } @Article{ Lvo78, Author = { M.N. L'vovskii }, Title = { {O}n the theory of harmonic maps with bounded dilatations }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 241 }, Pages = { 1024-1026 }, Year = { 1978 } } @Article{ Lab91, Author = { F. Labourie }, Title = { {E}xistence d'applications harmoniques tordues \`a valeurs dans les vari\'et\'es \`a courbure n\'egative }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 111 }, Pages = { 877-882 }, Year = { 1991 } } @Article{ Lad86, Author = { A. Lada }, Title = { {G}lobal analyticity of solutions of the {C}auchy problem for harmonic maps on two-dimensional {M}inkowski space }, Journal = { Bull.\ Polish Acad.\ Sci.\ Math. }, Volume = { 34 }, Pages = { 669-673 }, Year = { 1986 } } @Article{ Lad89, Author = { O.A. Ladyzhenskaya }, Title = { {T}riviality of harmonic mappings of finite energy of the {E}uclidean space {${\bf {R}}^m, m\geq 3$} into {R}iemannian manifolds }, Journal = { Algebra i Analiz }, Volume = { 1 }, Pages = { 114-115 }, Year = { 1989 } } @Article{ Lai92, Author = { I. Laine }, Title = { {H}armonic morphisms and non-linear potential theory }, Journal = { Banach Center Publ. }, Volume = { 27 }, Pages = { 271-275 }, Year = { 1992 } } @Article{ Lam67, Author = { K.Y. Lam }, Title = { {C}onstruction of nonsingular bilinear maps }, Journal = { Topology }, Volume = { 6 }, Pages = { 423-426 }, Year = { 1967 } } @Article{ Lam77, Author = { K.Y. Lam }, Title = { {S}ome interesting examples of nonsingular bilinear maps }, Journal = { Topology }, Volume = { 16 }, Pages = { 185-188 }, Year = { 1977 } } @Article{ Lam84, Author = { K.Y. Lam }, Title = { {T}opological methods for studying the composition of quadratic forms }, Journal = { Can.\ Math.\ Soc.\ Conf.\ Proc. }, Volume = { 4 }, Pages = { 173-192 }, Year = { 1984 } } @Article{ Lam85, Author = { K.Y. Lam }, Title = { {S}ome new results in compositions of quadratic forms }, Journal = { Invent.\ Math. }, Volume = { 79 }, Pages = { 467-474 }, Year = { 1985 } } @Misc{ LamPYi, Author = { K.Y. Lam and P.Yiu }, Title = { {B}eyond the impossibility of a 16-square identity } } @Article{ LamSmi93, Author = { T.Y. Lam and T.L. Smith }, Title = { {O}n {Y}uzvinsky's monomial pairing }, Journal = { Quart.\ J. Math.\ Oxford }, Volume = { 44 }, Pages = { 215-237 }, Year = { 1993 } } @Article{ LamTom87, Author = { D. Lambert and P. Tombal }, Title = { {H}yperbolic complex numbers and nonlinear sigma models }, Journal = { Internat.\ J. Theoret.\ Phys. }, Volume = { 26 }, Pages = { 943-950 }, Year = { 1987 } } @Article{ Lan91, Author = { J.M. Landsberg }, Title = { {M}inimal submanifolds of {${E}^{2n+1}$} arising from degenerate {${S}{O}(3)$} orbits on the {G}rassmannian }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 325 }, Pages = { 101-117 }, Year = { 1991 } } @Article{ Lan92, Author = { J.M. Landsberg }, Title = { {M}inimal submanifolds defined by first-order systems of {P}{D}{E} }, Journal = { J. Differential Geom. }, Volume = { 36 }, Pages = { 369-415 }, Year = { 1992 } } @Article{ Lan95, Author = { U. Lang }, Title = { {T}he existence of complete minimizing hypersurfaces in hyperbolic manifolds }, Journal = { Internat.\ J. Math. }, Volume = { 6 }, Pages = { 45-58 }, Year = { 1995 } } @Incollection{ Lan84, Author = { R. Langevin }, Title = { {E}nergies et g\'eom\'etrie int\'egrale }, Booktitle = { {D}ifferential {G}eometry }, Editor = { A.M. Naveira }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1045 }, Pages = { 95-103 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ LanRos88, Author = { R. Langevin and H. Rosenberg }, Title = { {A} maximum principle at infinity for minimal surfaces and applications }, Journal = { Duke Math.\ J. }, Volume = { 57 }, Pages = { 819-828 }, Year = { 1988 } } @Article{ LasRam96, Author = { B. Lasell and M. Ramachandran }, Title = { {O}bservations on harmonic maps and singular varieties }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 29 }, Pages = { 135-148 }, Year = { 1996 } } @Unpublished{ Law, Author = { H.B. Lawson }, Title = { {G}eometric aspects of the generalized {P}lateau problem }, Note = { preprint } } @Article{ Law69, Author = { H.B. Lawson }, Title = { {L}ocal rigidity theorems for minimal hypersurfaces }, Journal = { Ann.\ of Math. }, Volume = { 89 }, Pages = { 187-197 }, Year = { 1969 } } @Article{ Law70, Author = { H.B. Lawson }, Title = { {C}omplete minimal surfaces in {${S}^3$} }, Journal = { Ann.\ of Math. }, Volume = { 92 }, Pages = { 335-374 }, Year = { 1970 } } @Article{ Law70A, Author = { H.B. Lawson }, Title = { {T}he global behavior of minimal surfaces in {${S}^n$} }, Journal = { Ann.\ of Math. }, Volume = { 92 }, Pages = { 224-237 }, Year = { 1970 } } @Misc{ Law70B, Author = { H.B. Lawson }, Title = { {L}ectures on minimal submanifolds, {V}olume {I} }, Volume = { 14 }, Series = { IMPA Mono.\ de Mat. }, Year = { 1970 } } @Article{ Law70C, Author = { H.B. Lawson }, Title = { {R}igidity theorems in rank-1 symmetric spaces }, Journal = { J. Differential Geom. }, Volume = { 4 }, Pages = { 349-357 }, Year = { 1970 } } @Article{ Law70D, Author = { H.B. Lawson }, Title = { {T}he unknottedness of minimal embeddings }, Journal = { Invent.\ Math. }, Volume = { 11 }, Pages = { 183-7 }, Year = { 1970 } } @Article{ Law71, Author = { H.B. Lawson }, Title = { {T}he {R}iemannian geometry of holomorphic curves }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 2 }, Pages = { 45-62 }, Year = { 1971 } } @Book{ Law73, Author = { H.B. Lawson }, Title = { {M}inimal varieties in real and complex geometry }, Publisher = { Presses de Univ.\ Montr\'eal }, Year = { 1973 } } @Incollection{ Law75, Author = { H.B. Lawson }, Title = { {M}inimal varieties }, Booktitle = { {D}ifferential {G}eometry }, Editor = { S.S. Chern and R. Osserman }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 27 }, Pages = { 143-175 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1975 } } @Article{ Law85, Author = { H.B. Lawson }, Title = { {S}urfaces minimales et la construction de {C}alabi--{P}enrose }, Journal = { Ast{\'e}risque }, Volume = { 121--122 }, Pages = { 197-211 }, Year = { 1985 } } @Incollection{ Law87, Author = { H.B. Lawson }, Title = { {S}ous-vari\'et\'es associatives et courbes holomorphes dans {${S}^6$} }, Booktitle = { {T}h\'eorie des vari\'et\'es minimales et applications }, Volume = { 154/5 }, Pages = { 209-220 }, Series = { Ast\'erisque }, Year = { 1987 } } @Article{ LawOss77, Author = { H.B. Lawson and R. Osserman }, Title = { {N}on-existence, non-uniqueness and irregularity of solutions to the minimal surface system }, Journal = { Acta Math. }, Volume = { 139 }, Pages = { 1-17 }, Year = { 1977 } } @Article{ LawSim73, Author = { H.B. Lawson and J. Simons }, Title = { {O}n stable currents and their applications to global problems in real and complex geometry }, Journal = { Ann.\ of Math. }, Volume = { 98 }, Pages = { 427-450 }, Year = { 1973 } } @Unpublished{ LawTri, Author = { H.B. Lawson and R. Tribuzy }, Title = { {O}n the mean curvature function for compact functions }, Note = { preprint } } @Article{ LeB83, Author = { C. LeBrun }, Title = { {S}paces of complex null geodesics in complex-{R}iemannian geometry }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 278 }, Pages = { 209-231 }, Year = { 1983 } } @Article{ Leb84, Author = { C. Lebrun }, Title = { {T}wistor {C}{R} manifolds and three-dimensional conformal geometry. }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 284 }, Pages = { 601-616 }, Year = { 1984 } } @Article{ LedVan88, Author = { A.J. Ledger and L. Vanhecke }, Title = { {S}ymmetries on {R}iemannian manifolds }, Journal = { Math.\ Nachr. }, Volume = { 136 }, Pages = { 81-90 }, Year = { 1988 } } @Article{ LeeTot83, Author = { A. Lee and G. Toth }, Title = { {O}n variation spaces of harmonic maps into spheres }, Journal = { Acta Sci.\ Math.\ Hung. }, Volume = { 46 }, Pages = { 127-141 }, Year = { 1983 } } @Misc{ LeeWu, Author = { Y.I. Lee and D. Wu }, Title = { {O}n the existence of harmonic diffeomorphisms between complete surfaces } } @Article{ Lefadu95, Author = { C. Lefter and V. R{\v a}dulescu }, Title = { {T}he renormalized energy associated to a harmonic map }, Journal = { Panamer.\ Math.\ J. }, Volume = { 5 }, Pages = { 1-17 }, Year = { 1995 } } @Article{ Lei88, Author = { M.-L. Leite }, Title = { {H}armonic mappings of surfaces with respect to degenerate metrics }, Journal = { Amer.\ J. Math. }, Volume = { 110 }, Pages = { 399-412 }, Year = { 1988 } } @Article{ Lel73, Author = { J. Lelong-Ferrand }, Title = { {C}onstructions de modules de continuit\'e dans le cas limite de {S}oboleff et applications \`a la g\'eom\'etrie diff\'erentielle }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 52 }, Pages = { 297-311 }, Year = { 1973 } } @Article{ Lem74, Author = { L. Lemaire }, Title = { {A}pplications harmoniques de vari\'et\'es \`a bord }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 279 }, Pages = { 925-927 }, Year = { 1974 } } @Article{ Lem75, Author = { L. Lemaire }, Title = { {A}pplications harmoniques de surfaces }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 280 }, Pages = { 897-899 }, Year = { 1975 } } @Article{ Lem77, Author = { L. Lemaire }, Title = { {A}pplications harmoniques de vari\'et\'es produits }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 52 }, Pages = { 11-24 }, Year = { 1977 } } @Article{ Lem77A, Author = { L. Lemaire }, Title = { {H}armonic mappings of uniformly bounded dilatation }, Journal = { Topology }, Volume = { 16 }, Pages = { 199-201 }, Year = { 1977 } } @Article{ Lem78, Author = { L. Lemaire }, Title = { {A}pplications harmoniques de surfaces riemanniennes }, Journal = { J. Differential Geom. }, Volume = { 13 }, Pages = { 51-78 }, Year = { 1978 } } @Article{ Lem78A, Author = { L. Lemaire }, Title = { {H}armonic nonholomorphic maps from a surface to a sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 71 }, Pages = { 299-304 }, Year = { 1978 } } @Incollection{ Lem81, Author = { L. Lemaire }, Title = { {E}xistence des applications harmoniques et courbure des vari\'et\'es }, Booktitle = { {S}\'eminaire {B}ourbaki 553 (1979/80). {E}xp. 543--560 }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 842 }, Pages = { 174-195 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Incollection{ Lem81A, Author = { L. Lemaire }, Title = { {M}inima and critical points of the energy in dimension two }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Editor = { D. Ferus and W. K{\"u}hnel and U. Simon and B. Wegner }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 838 }, Pages = { 187-193 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Article{ Lem82, Author = { L. Lemaire }, Title = { {B}oundary value problems for harmonic and minimal maps of surfaces into manifolds }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 9 }, Pages = { 91-103 }, Year = { 1982 } } @Article{ Lem82A, Author = { L. Lemaire }, Title = { {H}armonic maps of finite energy from a complete surface to a compact manifold }, Journal = { Sympos.\ Math. }, Volume = { 26 }, Pages = { 23-26 }, Year = { 1982 } } @Article{ Lem85, Author = { L. Lemaire }, Title = { {T}he existence of harmonic maps }, Journal = { Curso de Mat.\ Recife }, Volume = { 23 }, Year = { 1985 } } @Incollection{ Lem93, Author = { L. Lemaire }, Title = { {A} note on exponentially harmonic maps }, Booktitle = { {P}roc. {S}hangai {S}ymp. 1991 }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 120-123 }, Year = { 1993 } } @Incollection{ Lem93A, Author = { L. Lemaire }, Title = { {O}n the non-existence of harmonic maps and solutions of an equation of {L}andau and {L}ifshitz }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 273-280 }, Year = { 1993 } } @Article{ LemWoo96, Author = { L. Lemaire and J.C. Wood }, Title = { {O}n the space of harmonic 2-spheres in {${\bf {C}} {P}^2$} }, Journal = { Internat.\ J. Math. }, Volume = { 7 }, Pages = { 211-225 }, Year = { 1996 } } @Misc{ LerSte, Author = { D. Lerner and I. Sterling }, Title = { {C}onstruction of constant mean curvature surfaces using the {D}{P}{W} representation of harmonic maps } } @Misc{ LesPeyZak, Author = { R.A. Lesse and M. Peyrard and W.J. Zakrzewski }, Title = { {S}oliton stability in the {${O}(3)$}\ {$\sigma$}-model in {$(2+1)$} dimensions } } @Unpublished{ Leu, Author = { M.C. Leung }, Title = { {L}iouville theorem for harmonic maps on asymptotically hyperbolic manifolds }, Note = { preprint } } @Unpublished{ LeuA, Author = { M.C. Leung }, Title = { {P}ositive solutions of second order quasilinear equations corresponding to {$p$}-harmonic maps }, Note = { preprint } } @Unpublished{ LeuB, Author = { M.C. Leung }, Title = { {R}otationally symmetric {$p$}-harmonic maps }, Note = { preprint dg-ga/9604006 } } @Unpublished{ Leu81, Author = { P.F. Leung }, Title = { {O}n stable currents, minimal submanifolds, and harmonic maps }, Note = { Notre Dame Ph.D Thesis }, Year = { 1981 } } @Incollection{ Leu82, Author = { P.F. Leung }, Title = { {O}n the stability of harmonic maps }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 122-129 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ Leu83, Author = { P.F. Leung }, Title = { {M}inimal submanifolds in a sphere }, Journal = { Math.\ Z. }, Volume = { 183 }, Pages = { 75-86 }, Year = { 1983 } } @Article{ Leu84, Author = { P.F. Leung }, Title = { {A} note on stable harmonic maps }, Journal = { J. London Math.\ Soc. }, Volume = { 29 }, Pages = { 380-384 }, Year = { 1984 } } @Article{ Leu91, Author = { P.F. Leung }, Title = { {M}inimal submanifolds in a sphere {I}{I} }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 23 }, Pages = { 387-390 }, Year = { 1991 } } @Article{ Lew36, Author = { H. Lewy }, Title = { {O}n the non-vanishing of the {J}acobian in certain one-to-one mappings }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 42 }, Pages = { 689-692 }, Year = { 1936 } } @Article{ Lew51, Author = { H. Lewy }, Title = { {O}n minimal surfaces with partially free boundaries }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 4 }, Pages = { 1-13 }, Year = { 1951 } } @Article{ Lew51A, Author = { H. Lewy }, Title = { {O}n the boundary behavior of minimal surfaces }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 37 }, Pages = { 103-110 }, Year = { 1951 } } @Article{ Lew68, Author = { H. Lewy }, Title = { {O}n the non-vanishing of the jacobian of a homeomorphism by harmonic gradients }, Journal = { Ann.\ of Math. }, Volume = { 88 }, Pages = { 518-529 }, Year = { 1968 } } @Incollection{ LeH87, Author = { Le~Hong~Van }, Title = { {M}inimal surfaces in homogeneous spaces }, Booktitle = { {D}iff. {G}eo. \& {A}ppl. {B}rno (1986) }, Publisher = { Univ.\ J.E. Purkyn{\v e} }, Address = { Brno }, Pages = { 199-212 }, Year = { 1987 } } @Article{ LeH88, Author = { Le~Hong~Van }, Title = { {A}bsolutely minimal surfaces and calibrations on the orbits of the adjoint representation of classical {L}ie groups }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 298 }, Pages = { 1308-1311 }, Year = { 1988 } } @Article{ LeH88A, Author = { Le~Hong~Van }, Title = { {M}inimal surfaces in homogeneous spaces }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 52 }, Pages = { 408-423, 447 }, Year = { 1988 } } @Article{ LeH88B, Author = { Le~Hong~Van }, Title = { {V}olumes of minimal surfaces and the curvature tensor of {R}iemannian manifolds }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 300 }, Pages = { 1308-1312 }, Year = { 1988 } } @Article{ LeH90, Author = { Le~Hong~Van }, Title = { {E}ach globally minimal surface in a compact homogeneous space has an invariant calibration }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 310 }, Pages = { 66-69 }, Year = { 1990 } } @Article{ LeH90A, Author = { Le~Hong~Van }, Title = { {J}acobi equations on minimal homogeneous submanifolds in homogeneous {R}iemannian spaces }, Journal = { Funktsional.\ Anal.\ i Prilozhen }, Volume = { 24 }, Pages = { 50-62 }, Year = { 1990 } } @Incollection{ LeH90B, Author = { Le~Hong~Van }, Title = { {R}elative calibrations and the problem of stability of minimal surfaces }, Booktitle = { {G}lobal {A}nalysis - {S}tudies and {A}pplications {I}{V} }, Editor = { Y.G. Borisovich and Y.E. Gliklikh }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1453 }, Pages = { 246-262 }, Series = { Lecture Notes in Math. }, Year = { 1990 } } @Article{ LeH93, Author = { Le~Hong~Van }, Title = { {A}pplications of integral geometry to minimal surfaces }, Journal = { Internat.\ J. Math. }, Volume = { 4 }, Pages = { 89-111 }, Year = { 1993 } } @Article{ LeH93A, Author = { Le~Hong~Van }, Title = { {C}urvature estimate for the volume growth of globally minimal surfaces }, Journal = { Math.\ Ann. }, Volume = { 296 }, Pages = { 103-118 }, Year = { 1993 } } @Article{ Li85, Author = { A.M. Li }, Title = { {A}n extrinsic rigidity theorem for minimal surfaces in {${S}^3$} }, Journal = { Math.\ Z. }, Volume = { 190 }, Pages = { 221-224 }, Year = { 1985 } } @Article{ LiZha94, Author = { A.M. Li and G.S Zhao }, Title = { {T}otally real minimal submanfolds in {${C}{P}^n$} }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 62 }, Pages = { 562-568 }, Year = { 1994 } } @Misc{ Li, Author = { J.F. Li }, Title = { {C}auchy problem of harmonic maps defined on {${S}^{1,1}$} } } @Article{ Li89, Author = { J.F. Li }, Title = { {T}he existence of closed geodesics on a complete {R}iemannian manifold }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 10 }, Pages = { 85-93 }, Year = { 1989 } } @Misc{ LiA, Author = { J.Y. Li }, Title = { {T}he heat flow and harmonic maps from complete manifolds into generalized regular balls } } @Misc{ LiB, Author = { J.Y. Li }, Title = { {H}eat flows and harmonic maps with a free boundary } } @Article{ Li93, Author = { J.Y. Li }, Title = { {T}he heat flow and harmonic maps of complete noncompact {R}iemannian manifolds }, Journal = { Math.\ Z. }, Volume = { 212 }, Pages = { 161-173 }, Year = { 1993 } } @Incollection{ Li93A, Author = { J.Y. Li }, Title = { {M}onotonicity formulas for {$p$}-harmonic maps from rotationally symmetric manifolds }, Booktitle = { {D}ifferential {G}eometry ({S}hanghai, 1991) }, Publisher = { World Sci.\ Publishing }, Address = { River Edge, NJ }, Pages = { 124-136 }, Year = { 1993 } } @Article{ Li94, Author = { J.Y. Li }, Title = { {H}eat flows and harmonic maps with a free boundary }, Journal = { Math.\ Z. }, Volume = { 217 }, Pages = { 487-495 }, Year = { 1994 } } @Article{ LiWan94, Author = { J.Y. Li and S. Wang }, Title = { {E}xistence of harmonic functions with finite energy on complete {R}iemannian manifolds }, Journal = { J. Partial Differential Equations }, Volume = { 7 }, Pages = { 257-263 }, Year = { 1994 } } @Misc{ LiWan, Author = { J.Y. Li and S.L. Wang }, Title = { {T}he heat flow of harmonic maps from noncompact manifolds } } @Article{ Li81, Author = { P. Li }, Title = { {M}inimal immersions of compact irreducible homogeneous {R}iemannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 16 }, Pages = { 105-115 }, Year = { 1981 } } @Article{ Li84, Author = { P. Li }, Title = { {U}niqueness of {${L}^1$} solutions for the {L}aplace equation and the heat equation on {R}iemannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 20 }, Pages = { 447-457 }, Year = { 1984 } } @Article{ Li85A, Author = { P. Li }, Title = { {F}unction theory on complete {R}iemannian manifolds }, Journal = { Ast{\'e}risque }, Volume = { 137 }, Pages = { 227-284 }, Year = { 1985 } } @Article{ Li86, Author = { P. Li }, Title = { {L}arge time behavior of the heat equation on complete manifolds with non-negative {R}icci curvature }, Journal = { Ann.\ of Math. }, Volume = { 124 }, Pages = { 1-21 }, Year = { 1986 } } @Incollection{ Li89A, Author = { P. Li }, Title = { {H}armonic maps of complete manifolds }, Booktitle = { {A}nalysis and geometry }, Publisher = { Korea Inst.\ Tech. }, Address = { Taejon }, Pages = { 67-82 }, Year = { 1989 } } @Book{ Li93B, Author = { P. Li }, Title = { {L}ecture notes on geometric analysis }, Publisher = { Seoul Nat.\ Univ. }, Address = { Seoul, Korea }, Volume = { 6 }, Series = { Lecture Notes Series, Seoul. }, Year = { 1993 } } @Incollection{ Li93C, Author = { P. Li }, Title = { {T}he theory of harmonic functions and its relation to geometry }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 307-315 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ LiSch84, Author = { P. Li and R. Schoen }, Title = { {${L}^p$} and mean value properties of subharmonic functions on {R}iemannian manifolds }, Journal = { Acta Math. }, Volume = { 153 }, Pages = { 279-301 }, Year = { 1984 } } @Article{ LiSchYau84, Author = { P. Li and R. Schoen and S.T. Yau }, Title = { {O}n the isoperimetric inequality for minimal surfaces }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 11 }, Pages = { 237-244 }, Year = { 1984 } } @Article{ LiTam87, Author = { P. Li and L.F. Tam }, Title = { {P}ositive harmonic functions on complete manifolds with non-negative curvature outside a compact set }, Journal = { Ann.\ of Math. }, Volume = { 125 }, Pages = { 171-207 }, Year = { 1987 } } @Article{ LiTam89, Author = { P. Li and L.F. Tam }, Title = { {L}inear growth harmonic functions on a complete manifold }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 421-425 }, Year = { 1989 } } @Article{ LiTam91, Author = { P. Li and L.F. Tam }, Title = { {T}he heat equation and harmonic maps of complete manifolds }, Journal = { Invent.\ Math. }, Volume = { 105 }, Pages = { 1-46 }, Year = { 1991 } } @Article{ LiTam92, Author = { P. Li and L.F. Tam }, Title = { {H}armonic functions and the structure of complete manifolds }, Journal = { J. Differential Geom. }, Volume = { 35 }, Pages = { 359-383 }, Year = { 1992 } } @Article{ LiTam93, Author = { P. Li and L.F. Tam }, Title = { {U}niqueness and regularity of proper harmonic maps {I} }, Journal = { Ann.\ of Math. }, Volume = { 137 }, Pages = { 167-201 }, Year = { 1993 } } @Article{ LiTam93A, Author = { P. Li and L.F. Tam }, Title = { {U}niqueness and regularity of proper harmonic maps {I}{I} }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 42 }, Pages = { 591-635 }, Year = { 1993 } } @Article{ LiTam95, Author = { P. Li and L.F. Tam }, Title = { {G}reen's function, {H}armonic function, and volume comparison }, Journal = { J. Differential Geom. }, Volume = { 41 }, Pages = { 277-318 }, Year = { 1995 } } @Article{ LiTamWan95, Author = { P. Li and L.F. Tam and J.P. Wang }, Title = { {H}armonic diffeomorphisms between {H}adamard manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 347 }, Pages = { 3645-3658 }, Year = { 1995 } } @Article{ LiYau82, Author = { P. Li and S.T. Yau }, Title = { {A} new conformal invariant and its applications to the {W}illmore conjecture and the first eigenvalue of compact surfaces }, Journal = { Invent.\ Math. }, Volume = { 69 }, Pages = { 269-291 }, Year = { 1982 } } @Article{ LiYau86, Author = { P. Li and S.T. Yau }, Title = { {O}n the parabolic kernel of {S}chr\"odinger operator }, Journal = { Acta Math. }, Volume = { 156 }, Pages = { 153-201 }, Year = { 1986 } } @Article{ Li95, Author = { X.X. Li }, Title = { {M}inimal immersions of {${S}^2$} into {${S}^{2m}(1)$} with degree {$2m+2$} }, Journal = { Kodai Math.\ J. }, Volume = { 18 }, Pages = { 351-364 }, Year = { 1995 } } @Misc{ LiC, Author = { X.Y. Li }, Title = { {C}onstruction of homogeneous harmonic maps from irreducible {H}ermitian symmetric spaces of compact type to quaternionic projective space } } @Misc{ LiD, Author = { X.Y. Li }, Title = { {R}elation between {U}hlenbeck's uniton and {C}hern and {W}olfson's {$\partial$}-transform } } @Misc{ LiE, Author = { X.Y. Li }, Title = { {S}tructure of pseudoholomorphic curves in complex {G}rassmann manifolds } } @Article{ Li94A, Author = { X.Y. Li }, Title = { {H}armonic maps from the two-sphere to a complex {G}rassmann manifold }, Journal = { Acta Math.\ Sinica }, Volume = { 37 }, Pages = { 387-392 }, Year = { 1994 } } @Article{ Li94B, Author = { Y.Y. Li }, Title = { {L}agrangian minimal surfaces in {K}{\"a}hler-{E}instein surfaces of negative curvature }, Journal = { Comm.\ Anal.\ Geom. }, Pages = { 579-592 }, Year = { 1994 } } @Article{ LiTia92, Author = { Y.Y. Li and G. Tian }, Title = { {R}egularity of harmonic maps with prescribed singularities }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 149 }, Pages = { 1-30 }, Year = { 1992 } } @Incollection{ LiTia93, Author = { Y.Y. Li and G. Tian }, Title = { {H}armonic maps with prescribed singularities }, Booktitle = { {D}ifferential {G}eometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { American Math.\ Soc. }, Volume = { 54 }, Pages = { 317-326 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1993 } } @Article{ Lia87, Author = { X. Liang }, Title = { {S}ome results on pseudo-embedded minimal surfaces in {${\bf {R}}^3$} }, Journal = { Acta Math.\ Sinica }, Volume = { 3 }, Pages = { 116-124 }, Year = { 1987 } } @Article{ Lia85, Author = { G.J. Liao }, Title = { {A} regularity theorem for harmonic maps with small energy }, Journal = { J. Differential Geom. }, Volume = { 22 }, Pages = { 233-241 }, Year = { 1985 } } @Article{ Lia88, Author = { G.J. Liao }, Title = { {A} study of regularity problem of harmonic maps }, Journal = { Pacific J. Math. }, Volume = { 131 }, Pages = { 291-302 }, Year = { 1988 } } @Article{ LiaTam92, Author = { G.J. Liao and L.F. Tam }, Title = { {O}n the heat equation for harmonic maps from non-compact manifolds }, Journal = { Pacific J. Math. }, Volume = { 153 }, Pages = { 129-145 }, Year = { 1992 } } @Incollection{ LiaSma93, Author = { G. Liao and N. Smale }, Title = { {H}armonic maps with nontrivial higher-dimensional singularities }, Booktitle = { {G}eometric analysis and nonlinear partial differential equations }, Editor = { I.J. Bakelman }, Publisher = { Dekker }, Address = { New York, Basel, Hong Kong }, Volume = { 144 }, Pages = { 79-89 }, Series = { Lecture Notes in Pure and Appl.\ Math. }, Year = { 1993 } } @Article{ Lia93, Author = { R.J. Liao }, Title = { {C}yclic properties of the harmonic sequence of surfaces in {${C}{P}^n$} }, Journal = { Math.\ Ann. }, Volume = { 296 }, Pages = { 363-384 }, Year = { 1993 } } @Article{ LibPau96, Author = { M. Libin and Y. Paul }, Title = { {R}egularity of {$n$}-harmonic maps }, Journal = { J. Geom.\ Anal. }, Volume = { 6 }, Pages = { 91-112 }, Year = { 1996 } } @Article{ Lic49, Author = { A. Lichnerowicz }, Title = { {Q}uelques th\'eor\`emes de g\'eom\'etrie diff\'erentielle globale }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 22 }, Pages = { 271-301 }, Year = { 1949 } } @Article{ Lic67, Author = { A. Lichnerowicz }, Title = { {V}ari\'et\'es k\"ahl\'eriennes et premi\`ere classe de {C}hern }, Journal = { J. Differential Geom. }, Volume = { 1 }, Pages = { 195-223 }, Year = { 1967 } } @Article{ Lic68, Author = { A. Lichnerowicz }, Title = { {S}ur les applications harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 267 }, Pages = { 548-553 }, Year = { 1968 } } @Article{ Lic69, Author = { A. Lichnerowicz }, Title = { {A}pplications harmoniques dans un tore }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 269 }, Pages = { 912-916 }, Year = { 1969 } } @Article{ Lic69A, Author = { A. Lichnerowicz }, Title = { {A}pplications harmoniques et vari\'et\'es k\"ahl\'eriennes }, Journal = { Rend.\ Sem.\ Mat.\ Fis.\ Milano }, Volume = { 39 }, Pages = { 186-195 }, Year = { 1969 } } @Article{ Lic69B, Author = { A. Lichnerowicz }, Title = { {V}ari\'et\'es k\"ahl\'eriennes \`a premi\`ere classe de {C}hern positive ou nulle }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 268 }, Pages = { 876-880 }, Year = { 1969 } } @Article{ Lic70, Author = { A. Lichnerowicz }, Title = { {A}pplications harmoniques et vari\'et\'es k\"ahl\'eriennes }, Journal = { Sympos.\ Math. }, Pages = { 341-402 }, Year = { 1970 } } @Article{ Lic71, Author = { A. Lichnerowicz }, Title = { {V}ari\'et\'es k\"ahl\'eriennes \`a premi\`ere classe de {C}hern non n\'egative et vari\'et\'es riemanniennes \`a courbure de {R}icci g\'en\'eralis\'ee non n\'egative }, Journal = { J. Differential Geom. }, Volume = { 6 }, Pages = { 47-94 }, Year = { 1971 } } @Article{ Lie92, Author = { G.M. Lieberman }, Title = { {O}n the regularity of the minimizer of a functional with exponential growth }, Journal = { Comment.\ Math.\ Univ.\ Carolin. }, Volume = { 33 }, Pages = { 45-49 }, Year = { 1992 } } @Article{ Lin, Author = { F.H. Lin }, Title = { {O}n the {D}irichlet problem for minimal graphs in hyperbolic space }, Journal = { Invent.\ Math. }, Volume = { 96 }, Pages = { 593-612 } } @Article{ Lin87, Author = { F.H. Lin }, Title = { {P}lateau's problem for {${H}$}-convex curves }, Journal = { Manuscripta Math. }, Volume = { 58 }, Pages = { 497-511 }, Year = { 1987 } } @Article{ Lin87A, Author = { F.H. Lin }, Title = { {U}ne remarque sur l'application {$x/\vert x\vert$} }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 305 }, Pages = { 529-531 }, Year = { 1987 } } @Article{ Lin88, Author = { F.H. Lin }, Title = { {E}xistence and regularity of embedded disks }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 553-560 }, Year = { 1988 } } @Incollection{ Lin91, Author = { F.H. Lin }, Title = { {N}ematic liquid crystals with variable degree of orientation }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 247-259 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Article{ Lin91A, Author = { F.H. Lin }, Title = { {O}n nematic liquid crystals with variable degree of orienation }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 44 }, Pages = { 453-468 }, Year = { 1991 } } @Incollection{ Lin93, Author = { F.H. Lin }, Title = { {S}ome recent results on harmonic maps to spheres }, Booktitle = { {D}ifferential {G}eometry: partial differential equations on manifolds }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { American Math.\ Soc. }, Address = { Providence RI }, Volume = { 54:1 }, Pages = { 327-331 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ Lin96, Author = { F.H. Lin }, Title = { {G}radient estimates and blow-up analysis for stationary harmonic maps }, Journal = { C. R. Acad.\ Sci.\ Paris S\'er.\ I Math. }, Volume = { 323 }, Pages = { 1005--1008 }, Year = { 1996 } } @Article{ LinXia88, Author = { F.H. Lin and C.Y. Xia }, Title = { {G}eometrical and topological obstructions of minimal hypersurfaces in {${S}^5$} }, Journal = { Kexue Tongbao (English Ed.) }, Volume = { 33 }, Pages = { 1409-1430 }, Year = { 1988 } } @Misc{ LinA, Author = { J.M. Lin }, Title = { {O}n the {H}einz inequality for the space like extremal surfaces in {${R}^{2,1}$} } } @Article{ Lin90, Author = { J.M. Lin }, Title = { {O}n the harmonic maps from {${\bf {R}}^2$} into {${H}^2$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 108 }, Pages = { 521-527 }, Year = { 1990 } } @Article{ LiuLiu94, Author = { G.L. Liu and H.L. Liu }, Title = { {R}otation surfaces with constant mean curvature in {$4$}-dimensional pseudo-{E}uclidean space }, Journal = { Kyushu J. Math. }, Volume = { 48 }, Pages = { 35-42 }, Year = { 1994 } } @Article{ Liu91, Author = { H.L. Liu }, Title = { {H}armonic indefinite metrics, harmonic tensors and harmonic immersions }, Journal = { Northeast.\ Math.\ J. }, Volume = { 7 }, Pages = { 397-405 }, Year = { 1991 } } @Article{ Liu92, Author = { H.L. Liu }, Title = { {M}inimal submanifolds and harmonic mappings of pseudo-{R}iemannian manifolds }, Journal = { J. Northeast.\ Univ.\ Tech. }, Volume = { 13 }, Pages = { 94-100 }, Note = { (Chinese, English summary) }, Year = { 1992 } } @Article{ LiuLia96, Author = { H. Liu and G.G. Liao }, Title = { {A} note on harmonic maps }, Journal = { Appl.\ Math.\ Lett. }, Volume = { 9 }, Pages = { 95--97 }, Year = { 1996 } } @Unpublished{ Liu68, Author = { M.C. Liu }, Title = { {H}eat equations on {R}iemannian connected bundles }, Note = { Washington Univ. Thesis }, Year = { 1968 } } @Article{ Liu73, Author = { M.C. Liu }, Title = { {T}otally geodesic fibre maps }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 79 }, Pages = { 150-151 }, Year = { 1973 } } @Article{ Log87, Author = { M.Y. Logachev }, Title = { {I}nvestigation of the ambiguity of a fixed gauge by means of the theory of harmonic mappings }, Journal = { Teoret.\ Mat.\ Fiz. }, Volume = { 70 }, Pages = { 412-421 }, Year = { 1987 } } @Misc{ Loh, Author = { J. Lohkamp }, Title = { {H}armonic diffeomorphisms and {T}eichm\"uller theory } } @Article{ Loh90, Author = { J. Lohkamp }, Title = { {A}n existence theorem for harmonic maps }, Journal = { Manuscripta Math. }, Volume = { 67 }, Pages = { 21-23 }, Year = { 1990 } } @Misc{ Loo, Author = { B. Loo }, Title = { {O}n involutions and {C}alabi liftings } } @Misc{ LooA, Author = { B. Loo }, Title = { {O}n the compactification of the moduli space of branched minimal immersions of {${S}^2$} into {${S}^4$} } } @Article{ Loo89, Author = { B. Loo }, Title = { {T}he space of harmonic maps of {${S}^2$} into {${S}^4$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 313 }, Pages = { 81-102 }, Year = { 1989 } } @Article{ LooVai94, Author = { B. Loo and I. Vainsencher }, Title = { {L}imits of graphs }, Journal = { Mat.\ Contemp. }, Volume = { 6 }, Pages = { 41-59 }, Year = { 1994 } } @Article{ Lop92, Author = { F.J. Lopez }, Title = { {T}he classification of complete minimal surfaces with total curvature greater than {$-12\pi$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 334 }, Pages = { 49-74 }, Year = { 1992 } } @Article{ LopRos89, Author = { F.J. Lopez and A. Ros }, Title = { {C}omplete minimal surfaces with index one and stable constant mean curvature surfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 64 }, Pages = { 34-43 }, Year = { 1989 } } @Article{ Lu93, Author = { D. Lu }, Title = { {H}omogeneous foliations of spheres }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 340 }, Pages = { 94-102 }, Year = { 1993 } } @Article{ Lu68, Author = { Y.C. Lu }, Title = { {H}olomorphic mappings of complex manifolds }, Journal = { J. Differential Geom. }, Volume = { 2 }, Pages = { 299-312 }, Year = { 1968 } } @Misc{ Luc, Author = { S. Luckhaus }, Title = { {${C}^{1,k}$}-regularity for energy minimizing {H}\"older continuous {$p$}-harmonic maps between {R}iemannian manifolds } } @Unpublished{ LucA, Author = { S. Luckhaus }, Title = { {T}he {D}ouglas-problem for surfaces of prescribed mean curvature }, Note = { preprint } } @Article{ Luc88, Author = { S. Luckhaus }, Title = { {P}artial {H}\"older continuity for energy minimizing {$p$}-harmonic maps between {R}iemannian maniolds }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 37 }, Pages = { 349-367 }, Year = { 1988 } } @Article{ Luc93, Author = { S. Luckhaus }, Title = { {C}onvergence of minimizers for the {$p$}-{D}irichlet integral }, Journal = { Math.\ Z. }, Volume = { 213 }, Pages = { 449-456 }, Year = { 1993 } } @Article{ LudOkuYan75, Author = { G.D. Ludden and M. Okumura and K. Yano }, Title = { {A} totally real surface on {${C}{P}^2$} that is not totally geodesic }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 53 }, Pages = { 186-190 }, Year = { 1975 } } @Incollection{ Luk, Author = { J. Lukierski }, Title = { {F}our dimensional quaternionic {$\sigma$}-models }, Booktitle = { {F}ield theoretical methods in particle physics ({K}aiserstauten, 1979) }, Publisher = { Plenum }, Address = { New York }, Volume = { 55 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ B: Phys. } } @Article{ Lyz91, Author = { A. Lyzzaik }, Title = { {O}n the valence of some classes of harmonic maps }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 110 }, Pages = { 313-325 }, Year = { 1991 } } @Article{ LopRos91, Author = { F.J. L{\'o}pez and A. Ros }, Title = { {O}n embedded complete minimal surfaces of genus zero }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 293-300 }, Year = { 1991 } } @Misc{ Ma, Author = { L. Ma }, Title = { {T}he {D}irichlet problem at infinity for locally minimizing harmonic maps } } @Misc{ MaA, Author = { L. Ma }, Title = { {E}xamples of harmonic map heat flow in dimension two } } @Misc{ MaB, Author = { L. Ma }, Title = { {H}armonic maps with prescribed finite singularities } } @Unpublished{ Ma89, Author = { L. Ma }, Title = { {P}lateau problem for harmonic maps }, Note = { Preprint, Peking Univ. }, Year = { 1989 } } @Article{ Ma90, Author = { L. Ma }, Title = { {A}pplications harmoniques \`a valeurs dans une vari\'et\'e lorentzienne }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 311 }, Pages = { 437-442 }, Year = { 1990 } } @Article{ Ma91, Author = { L. Ma }, Title = { {H}armonic map heat flow with free boundary }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 66 }, Pages = { 279-301 }, Year = { 1991 } } @Article{ Ma91A, Author = { L. Ma }, Title = { {O}n equivariant harmonic maps defined on a {L}orentz manifold }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) }, Volume = { 41 }, Pages = { 511-518 }, Year = { 1991 } } @Article{ Ma93, Author = { L. Ma }, Title = { {R}egularity of minimizing harmonic maps into ellipsoids }, Journal = { Acta Math.\ Sinica (N.S.) }, Volume = { 9 }, Pages = { 63-69 }, Year = { 1993 } } @Article{ Ma95, Author = { L. Ma }, Title = { {P}artial regularity of energy minimizing harmonic maps into a complete manifold }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 3 }, Pages = { 513-529 }, Year = { 1995 } } @Article{ MaZha93, Author = { Z.S. Ma and Y.H. Zhang }, Title = { {S}pherical minimal submanifolds in which the second standard immersion of the sphere is of {$3$}-type }, Journal = { Sichuan Shifa Daxue Xuebao Ziran Kexue Ban }, Volume = { 16 }, Pages = { 7-12 }, Year = { 1993 } } @Article{ Mac92, Author = { E. Macias-Virg{\'o}s }, Title = { {M}inimal foliations on {L}ie groups }, Journal = { Indag.\ Math. }, Volume = { 3 }, Pages = { 41-46 }, Year = { 1992 } } @Article{ Mae86, Author = { S. Maeda }, Title = { {R}emarks on isotropic immersions }, Journal = { Yokohama Math.\ J. }, Volume = { 34 }, Pages = { 83-90 }, Year = { 1986 } } @Article{ MaeTsu94, Author = { S. Maeda and K. Tsukuda }, Title = { {I}sotropic immersions into a real space form }, Journal = { Canad.\ Math.\ Bull. }, Volume = { 37 }, Pages = { 245-253 }, Year = { 1994 } } @Article{ Mai, Author = { J.M. Mailler }, Title = { {K}ac-{M}oody algebra and extended {Y}ang-{B}axter relations in the {${O}({N})$} nonlinear {$\sigma$}-model }, Journal = { Phys.\ Lett. }, Volume = { B 162 }, Pages = { 137-142 } } @Article{ Mai79, Author = { D. Maison }, Title = { {E}hler--{H}arrison type transformations for {J}ordan's extended theory of gravitation }, Journal = { Gen.\ Relativity Gravitation }, Volume = { 10 }, Pages = { 717-723 }, Year = { 1979 } } @Article{ Man92, Author = { H. Manabe }, Title = { {P}luriharmonic maps into principal fiber bundle and vertical torsion }, Journal = { Tsukuba J. Math. }, Volume = { 16 }, Pages = { 191-202 }, Year = { 1992 } } @Unpublished{ ManMus88, Author = { G. Mancini and R. Musina }, Title = { {S}urfaces of minimal area enclosing a given body in {${\bf {R}}^3$} }, Note = { Preprint, SISSA }, Year = { 1988 } } @Incollection{ ManMus90, Author = { G. Mancini and R. Musina }, Title = { {S}urfaces of minimal area supported by a given boundary in {${\bf {R}}^3$} }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 319-337 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Article{ ManVes94, Author = { J.J. Manfredi and V. Vespri }, Title = { {$n$}-harmonic morphisms in space are {M}{\"o}bius transformations }, Journal = { Michigan Math.\ J. }, Volume = { 41 }, Pages = { 135-142 }, Year = { 1994 } } @Article{ ManMil91, Author = { B.M. Mann and R.J. Milgram }, Title = { {S}ome spaces of holomorphic maps to complex {G}rassmannian manifolds }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 301-324 }, Year = { 1991 } } @Article{ ManMil93, Author = { B.M. Mann and R.J. Milgram }, Title = { {O}n the moduli space of {${S}{U}(n)$} monopoles and holomorphic maps to flag manifolds }, Journal = { J. Differential Geom. }, Volume = { 38 }, Pages = { 39-103 }, Year = { 1993 } } @Misc{ Man, Author = { N.S. Manton }, Title = { {G}eometry of {S}kyrmions } } @Misc{ ManRub, Author = { N.S. Manton and P.J. Ruback }, Title = { {S}kyrmions in flat space and curved space } } @Article{ Mar89, Author = { H. Marbes }, Title = { {O}n the set of umbilical points of a twistor-holomorphic immersion into {${\bf {R}}^4$} }, Journal = { Math.\ Nachr. }, Volume = { 142 }, Pages = { 19-26 }, Year = { 1989 } } @Misc{ Mar, Author = { P. March }, Title = { {T}he limiting angle of certain {R}iemannian {B}rownian motions: {R}elations with {D}irichlet problem at infinity } } @Article{ Mar86, Author = { P. March }, Title = { {B}rownian motion and harmonic functions on rotationally symmetric manifolds }, Journal = { Ann.\ Probab. }, Volume = { 14 }, Pages = { 793-801 }, Year = { 1986 } } @Article{ Mar93, Author = { V.R. Marenich }, Title = { {O}n existence of harmonic maps from a surface to the space of its normal bundle }, Journal = { Math.\ Z. }, Volume = { 214 }, Pages = { 373-375 }, Year = { 1993 } } @Incollection{ Mar88, Author = { C. Margerin }, Title = { {\'{E}}l{\'e}ments pour une th{\'e}orie de al r{\'e}gularit{\'e} des applications harmonique }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 26-78 }, Year = { 1988 } } @Article{ Mar78, Author = { V. Marino }, Title = { {A}pplicazioni armoniche e connessioni tensoriali secondo {B}ompiani }, Journal = { Rend.\ Mat. }, Volume = { 6 }, Pages = { 405-411 }, Year = { 1978 } } @Article{ Mar86A, Author = { S. Markvorsen }, Title = { {O}n the heat kernel comparison theorems for minimal submanifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 97 }, Pages = { 479-482 }, Year = { 1986 } } @Incollection{ Mar88A, Author = { S. Markvorsen }, Title = { {A} transplantation of heat kernel via harmonic maps }, Booktitle = { {P}roc. {V}{I} {I}nter. {C}oll. {D}iff. {G}eom. {S}antiago }, Publisher = { Univ.\ de Santiago }, Address = { Santiago de Compostela }, Volume = { 61 }, Pages = { 171-175 }, Series = { Cursos e Congresos de Univ.\ de Santiago }, Year = { 1988 } } @Article{ Mar89A, Author = { S. Markvorsen }, Title = { {O}n the mean exit time from a minimal submanifold }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 1-8 }, Year = { 1989 } } @Article{ MarReiSal79, Author = { M. Martellini and C. Reina and P. Salano }, Title = { {A} first order system of differential equations for covariant {$\sigma$}-models }, Journal = { J. Math.\ Phys. }, Volume = { 20 }, Pages = { 2619-2620 }, Year = { 1979 } } @Article{ Mar77, Author = { H.H. Martens }, Title = { {A} remark on {A}bel's theorem and the mapping of linear series }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 52 }, Pages = { 557-559 }, Year = { 1977 } } @Article{ Mar78A, Author = { H.H. Martens }, Title = { {O}bservations on morphisms of closed {R}iemann surfaces }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 10 }, Pages = { 209-212 }, Year = { 1978 } } @Misc{ MarA, Author = { A. Martinez }, Title = { {N}ew examples of minimal tori in {${S}^3$} } } @Article{ Mar95, Author = { J.C. Martinez }, Title = { {M}inimal surfaces, incompressible flows and the geometric phase }, Journal = { Phys.\ Lett.\ A }, Volume = { 204 }, Pages = { 205-209 }, Year = { 1995 } } @Misc{ Mas, Author = { K. Mashimo }, Title = { {S}table minimal cones in {${\bf {R}}^7$} } } @Article{ Mas80, Author = { K. Mashimo }, Title = { {D}egree of the standard isometric minimal immersions of complex projective spaces into spheres }, Journal = { Tsukuba J. Math. }, Volume = { 4 }, Pages = { 133-145 }, Year = { 1980 } } @Article{ Mas84, Author = { K. Mashimo }, Title = { {M}inimal immersions of a {$3$}-dimensional sphere into spheres }, Journal = { Osaka J. Math. }, Volume = { 21 }, Pages = { 721-732 }, Year = { 1984 } } @Article{ Mas88, Author = { K. Mashimo }, Title = { {E}igenmaps and minimal immersions of projective spaces into spheres }, Journal = { T\^ohoku Math.\ J. }, Volume = { 40 }, Pages = { 245-267 }, Year = { 1988 } } @Unpublished{ Mas95, Author = { K. Mashimo }, Title = { {S}pectra of the {L}aplacian on the {C}ayley projective plane }, Note = { Preprint }, Year = { 1995 } } @Article{ MasTas91, Author = { K. Mashimo and H. Tasaki }, Title = { {S}tability of closed {L}ie subgroups in compact {L}ie groups }, Journal = { Kodai Math.\ J. }, Volume = { 13 }, Pages = { 181-203 }, Year = { 1991 } } @Book{ MasMir84, Author = { U. Massari and M. Miranda }, Title = { {M}inimal surfaces of codimension one }, Publisher = { North Holland }, Volume = { 91 }, Series = { Notes }, Year = { 1984 } } @Article{ Mas89, Author = { R. Masuoka }, Title = { {O}n the stability of {R}iemannian manifolds }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 41 }, Pages = { 493-501 }, Year = { 1989 } } @Article{ MasWol95, Author = { H.A. Masur and M. Wolf }, Title = { {T}eichm\"uller space is not {G}romov hyperbolic }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { 20 }, Pages = { 259-267 }, Year = { 1995 } } @Article{ MatPle94, Author = { T. Matos and J. Plebanski }, Title = { {A}xisymmetric stationary solutions as harmonic maps }, Journal = { Gen.\ Relativity Gravitation }, Volume = { 26 }, Pages = { 477-498 }, Year = { 1994 } } @Article{ MatNic94, Author = { H.J. Matschull and H. Nicolai }, Title = { {C}anonical treatment of coset space sigma models }, Journal = { Internat.\ J. Modern Phys.\ D }, Volume = { 3 }, Year = { 1994 } } @Article{ Mat71, Author = { Y. Matsushima }, Title = { {V}ector bundle valued harmonic forms and immersions of {R}iemannian manifolds }, Journal = { Osaka J. Math. }, Volume = { 8 }, Pages = { 1-13 }, Year = { 1971 } } @Article{ Mat74, Author = { Y. Matsushima }, Title = { {H}olomorphic immersions of a compact {K}\"ahler manifold into complex tori }, Journal = { J. Differential Geom. }, Volume = { 9 }, Pages = { 309-328 }, Year = { 1974 } } @Article{ Mat80, Author = { Y. Matsuyama }, Title = { {M}inimal submanifolds in {${S}^{N}$} or {${R}^{N}$} }, Journal = { Math.\ Z. }, Volume = { 175 }, Pages = { 275-282 }, Year = { 1980 } } @Article{ Mat82, Author = { Y. Matsuyama }, Title = { {S}ome remarks on minimal submanifolds in {${S}^{N}$} or {${R}^{N}$} }, Journal = { Bull.\ Fac.\ Sci.\ Engrg.\ Chuo Univ.\ Ser.\ I Math. }, Volume = { 25 }, Pages = { 1-2 }, Year = { 1982 } } @Article{ Mat93, Author = { Y. Matsuyama }, Title = { {M}inimal {E}instein submanifolds with codimension 2 }, Journal = { Tensor (N.S.) }, Volume = { 52 }, Pages = { 61-68 }, Year = { 1993 } } @Incollection{ Mat93A, Author = { Y. Matsuyama }, Title = { {O}n some pinchings of minimal submanifolds }, Booktitle = { {G}eo. and its {A}ppl. }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 121-134 }, Year = { 1993 } } @Incollection{ May81, Author = { M.E. Mayer }, Title = { {T}he geometry of symmetry breaking in gauge theories }, Booktitle = { {N}ew developments in physics, {S}chladming 1981 }, Publisher = { Springer }, Volume = { XXIII }, Pages = { 477-490 }, Series = { Acta Phys.\ Austriaca Suppl. }, Year = { 1981 } } @Misc{ May, Author = { U.F. Mayer }, Title = { {G}radient flows on nonpositively curved metric spaces } } @Article{ Maz73, Author = { E. Mazet }, Title = { {L}a formule de la variation seconde de l'\'energie au voisinage d'une application harmonique }, Journal = { J. Differential Geom. }, Volume = { 8 }, Pages = { 279-296 }, Year = { 1973 } } @Article{ Maz82, Author = { P.O. Mazur }, Title = { {P}roof of uniqueness of the {K}err--{N}ewman black hole solution }, Journal = { J. Phys.\ A }, Volume = { 15 }, Pages = { 3173-3180 }, Year = { 1982 } } @Article{ Maz84, Author = { P.O. Mazur }, Title = { {A} global identity for nonlinear {$\sigma$}-models }, Journal = { Phys.\ Lett.\ A }, Volume = { 100 }, Pages = { 341-344 }, Year = { 1984 } } @Article{ MazRic85, Author = { P.O. Mazur and E. Richter }, Title = { {H}armonic maps and uniqueness of axisymmetric monopole solutions }, Journal = { Phys.\ Lett.\ A }, Volume = { 109 }, Pages = { 429-432 }, Year = { 1985 } } @Incollection{ Man94, Author = { M. Ma{\~n}as }, Title = { {T}he principal chiral model as an integrable system }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 147-173 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ McC91, Author = { P.A. McCoy }, Title = { {R}epresentation of harmonic functions in {${\bf {R}}^4$} }, Journal = { J. Math.\ Anal.\ Appl. }, Volume = { 154 }, Pages = { 43-54 }, Year = { 1991 } } @Article{ McI96, Author = { I. McIntosh }, Title = { {T}wo remarks on the construction of harmonic tori in {${\bf {C}{P}}^n$} }, Journal = { Internat.\ J. Math. }, Volume = { 7 }, Pages = { 515-520 }, Year = { 1996 } } @Article{ McI94, Author = { I.R. McIntosh }, Title = { {G}lobal solutions of the elliptic 2{D} {T}oda lattice }, Journal = { Nonlinearity }, Volume = { 7 }, Pages = { 85-108 }, Year = { 1994 } } @Incollection{ McI94A, Author = { I.R. McIntosh }, Title = { {I}nfinite dimensional {L}ie groups and the two-dimensional {T}oda lattice }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 205-220 }, Series = { Aspects of Math. }, Year = { 1994 } } @Unpublished{ McI94B, Author = { I.R. McIntosh }, Title = { {O}n the existence of superconformal {$2$}-tori in complex projective space }, Note = { Bath preprint }, Year = { 1994 } } @Article{ McI95, Author = { I.R. McIntosh }, Title = { {A} construction of all non-isotropic harmonic tori in complex projective space }, Journal = { Internat.\ J. Math. }, Volume = { 6 }, Pages = { 831-879 }, Year = { 1995 } } @Article{ McI85, Author = { R. McIntosh }, Title = { {S}ingular area minimizing hypersurfaces }, Journal = { Austral.\ Math.\ Soc.\ Gaz. }, Volume = { 22 }, Pages = { 233-241 }, Year = { 1985 } } @Article{ McISim90, Author = { R. McIntosh and L. Simon }, Title = { {P}erturbing away singularities of harmonic maps }, Journal = { Manuscripta Math. }, Volume = { 67 }, Pages = { 113-124 }, Year = { 1990 } } @Unpublished{ Mee75, Author = { W.H. Meeks }, Title = { {T}he conformal structure and geometry of triply periodic minimal surfaces in {${\bf {R}}^3$} }, Note = { Univ. California at Berkeley Ph.D Thesis }, Year = { 1975 } } @Article{ Mee77, Author = { W.H. Meeks }, Title = { {T}he conformal structure and geometry of triply periodic minimal surfaces in {${\bf {R}}^3$} }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 83 }, Pages = { 134-136 }, Year = { 1977 } } @Unpublished{ Mee78, Author = { W.H. Meeks }, Title = { {L}ectures on {P}lateau's problem }, Note = { I.M.P.A. notes }, Year = { 1978 } } @Article{ Mee81, Author = { W.H. Meeks }, Title = { {T}he classification of complete minimal surfaces with total curvature greater than {$-8\{P}i$} }, Journal = { Duke Math.\ J. }, Volume = { 48 }, Pages = { 523-535 }, Year = { 1981 } } @Article{ Mee81A, Author = { W.H. Meeks }, Title = { {A} survey of the geometric results in the classical theory of minimal surfaces }, Journal = { Bol.\ Soc.\ Brasil.\ Mat. }, Volume = { 12 }, Pages = { 29-86 }, Year = { 1981 } } @Article{ Mee81B, Author = { W.H. Meeks }, Title = { {T}he topological uniqueness of minimal surfaces in three dimensional {E}uclidean space }, Journal = { Topology }, Volume = { 20 }, Pages = { 389-410 }, Year = { 1981 } } @Article{ Mee81C, Author = { W.H. Meeks }, Title = { {U}niqueness theorem for minimal surfaces {I}ll }, Journal = { J. Math. }, Volume = { 25 }, Pages = { 318-336 }, Year = { 1981 } } @Incollection{ Mee87, Author = { W.H. Meeks }, Title = { {R}ecent progress on the geometry of surfaces in {${\bf {R}}^3$} and on the use of computer graphics as a research tool }, Booktitle = { {P}roc. {I}. {C}. {M}. }, Pages = { 551-560 }, Year = { 1987 } } @Article{ Mee87A, Author = { W.H. Meeks }, Title = { {T}he topology and geometry of embedded surfaces of constant mean curvature }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 17 }, Pages = { 315-317 }, Year = { 1987 } } @Article{ Mee88, Author = { W.H. Meeks }, Title = { {T}he topology and geometry of embedded surfaces of constant mean curvature }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 539-552 }, Year = { 1988 } } @Article{ Mee89, Author = { W.H. Meeks }, Title = { {R}egularity of the {A}lbanese map for nonorientable surfaces }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 345-352 }, Year = { 1989 } } @Article{ Mee90, Author = { W.H. Meeks }, Title = { {T}he theory of triply-periodic minimal surfaces }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 39 }, Pages = { 877-936 }, Year = { 1990 } } @Incollection{ Mee93, Author = { W.H. Meeks }, Title = { {T}he geometry, topology and existence of periodic minimal surfaces }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 333-374 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ MeeRos, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he maximum principle at infinity for minimal surfaces in flat three-manifolds }, Journal = { Comment.\ Math.\ Helv. } } @Misc{ MeeRosA, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he strong maximum principle for complete minimal surfaces in flat {$3$}-manifolds } } @Article{ MeeRos88, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he geometry and topology of doubly periodic minimal surfaces }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 306 }, Pages = { 605-609 }, Year = { 1988 } } @Article{ MeeRos89, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he global theory of doubly periodic minimal surfaces }, Journal = { Invent.\ Math. }, Volume = { 97 }, Pages = { 351-379 }, Year = { 1989 } } @Article{ MeeRos93, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he geometry and conformal structure of properly embedded minimal surfaces of finite topology in {${\bf {R}}^3$} }, Journal = { Invent.\ Math. }, Volume = { 114 }, Pages = { 625-639 }, Year = { 1993 } } @Article{ MeeRos93A, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he geometry of periodic minimal surfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 68 }, Pages = { 538-578 }, Year = { 1993 } } @Article{ MeeRos93B, Author = { W.H. Meeks and H. Rosenberg }, Title = { {T}he geometry of periodic minimal surfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 68 }, Pages = { 538-578 }, Year = { 1993 } } @Article{ MeeSco86, Author = { W.H. Meeks and W.P. Scott }, Title = { {F}inite group actions on {$3$}-manifolds }, Journal = { Invent.\ Math. }, Volume = { 86 }, Pages = { 287-346 }, Year = { 1986 } } @Article{ MeeSimYau82, Author = { W.H. Meeks and L. Simon and S.T. Yau }, Title = { {E}mbedded minimal surfaces, exotic spheres, and manifolds with positive {R}icci curvature }, Journal = { Ann.\ of Math. }, Volume = { 116 }, Pages = { 621-659 }, Year = { 1982 } } @Article{ MeeWhi91, Author = { W.H. Meeks and B. White }, Title = { {M}inimal surfaces bounded by convex curves in parallel planes }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 66 }, Pages = { 263-278 }, Year = { 1991 } } @Article{ MeeWhi93, Author = { W.H. Meeks and B.C. White }, Title = { {T}he space of minimal annuli bounded by an extremal pair of planar curves }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 415-437 }, Year = { 1993 } } @Misc{ MeeYau, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}he topological uniqueness theorem of complete minimal surfaces of finite topological type } } @Incollection{ MeeYau78, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}he classical {P}lateau problem and the topology of {$3$}-manifolds }, Booktitle = { {M}inimal submanifolds and {G}eodesics }, Editor = { M. Obata }, Publisher = { Kaigai Publ. }, Address = { Tokyo }, Pages = { 101-102 }, Year = { 1978 } } @Article{ MeeYau80, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}opology of three dimensional manifolds and the embedding problems in minimal surface theory }, Journal = { Ann.\ of Math. }, Volume = { 112 }, Pages = { 441-484 }, Year = { 1980 } } @Article{ MeeYau81, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}he equivariant {D}ehn's lemma and loop theorem }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 56 }, Pages = { 225-239 }, Year = { 1981 } } @Article{ MeeYau82, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}he classical {P}lateau problem and the topology of three dimensional manifolds }, Journal = { Topology }, Volume = { 21 }, Pages = { 408-442 }, Year = { 1982 } } @Article{ MeeYau82A, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}he existence of embedded minimal surfaces and the problem of uniqueness }, Journal = { Math.\ Z. }, Volume = { 179 }, Pages = { 151-168 }, Year = { 1982 } } @Incollection{ MeeYau84, Author = { W.H. Meeks and S.T. Yau }, Title = { {T}he equivariant loop theorem for three dimensional manifolds and a review of the existence theorems for minimal surfaces }, Booktitle = { {T}he {S}mith {C}onjecture ({N}ew {Y}ork 1979) }, Publisher = { Academic Press }, Address = { Orlando, Fla. }, Volume = { 112 }, Pages = { 167-179 }, Series = { Pure Appl.\ Math. }, Year = { 1984 } } @Incollection{ MeeYau84A, Author = { W.H. Meeks and S.T. Yau }, Title = { {G}roup actions on {${\bf {R}}^3$} }, Booktitle = { {T}he {S}mith {C}onjecture ({N}ew {Y}ork 1979) }, Publisher = { Academic Press }, Address = { Orlando, Fla. }, Volume = { 112 }, Pages = { 167-179 }, Series = { Pure Appl.\ Math. }, Year = { 1984 } } @Misc{ MeeYi, Author = { W.H. Meeks and F. Yi }, Title = { {A} note on the geometry of minimal annuli in {${\bf {R}}^3$} } } @Article{ Mei79, Author = { M. Meier }, Title = { {L}iouville theorems for nonlinear equations and systems }, Journal = { Manuscripta Math. }, Volume = { 29 }, Pages = { 207-228 }, Year = { 1979 } } @Article{ Mei82, Author = { M. Meier }, Title = { {B}oundedness and integrability properties of weak solutions of quasilinear elliptic systems }, Journal = { J. Reine Angew.\ Math. }, Volume = { 333 }, Pages = { 191-220 }, Year = { 1982 } } @Article{ Mei83, Author = { M. Meier }, Title = { {R}emovable singularities for weak solutions of quasilinear elliptic systems }, Journal = { J. Reine Angew.\ Math. }, Volume = { 344 }, Pages = { 87-101 }, Year = { 1983 } } @Article{ Mei86, Author = { M. Meier }, Title = { {R}emovable singularities of harmonic maps and an application to minimal submanifolds }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 35 }, Pages = { 705-726 }, Year = { 1986 } } @Unpublished{ Mei88, Author = { M. Meier }, Title = { {A}symptotic behavior of solutions of some quasilinear elliptic systems in exterior domains }, Note = { SFB254 Bonn }, Year = { 1988 } } @Article{ Mel93, Author = { A.D. Melas }, Title = { {A}n example of a harmonic map between {E}uclidean balls }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 117 }, Pages = { 857-859 }, Year = { 1993 } } @Incollection{ MelSte94, Author = { M. Melko and I. Sterling }, Title = { {I}ntegrable systems, harmonic maps and the classical theory of solitons }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 129-144 }, Series = { Aspects of Math. }, Year = { 1994 } } @Incollection{ Men92, Author = { O.F. Menshikh }, Title = { {O}n a generalization of {W}eirstrass formula in the theory of minimal surfaces }, Booktitle = { {A}rithmetic and {G}eometry of {M}anifolds }, Editor = { E.V. Voskresenskij }, Publisher = { Samar.\ Gos.\ Univ. }, Address = { Samara }, Pages = { 93-100 }, Year = { 1992 } } @Incollection{ Mey81, Author = { P.A. Meyer }, Title = { {G}\'eom\'etrie stochastique sans larmes }, Booktitle = { {S}\'eminaire de {P}robabilit\'es {X}{V}, (1979/80) }, Editor = { J. Az{\'e}ma and M. Yor }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 850 }, Pages = { 44-102 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Misc{ Mic, Author = { M. Micallef }, Title = { {M}inimal surfaces in flat tori } } @Misc{ MicA, Author = { M.J. Micallef }, Title = { {O}n the topology of positively curved manifolds } } @Article{ Mic84, Author = { M.J. Micallef }, Title = { {S}table minimal surfaces in {E}uclidean space }, Journal = { J. Differential Geom. }, Volume = { 19 }, Pages = { 57-84 }, Year = { 1984 } } @Article{ Mic85, Author = { M.J. Micallef }, Title = { {A} note on branched stable two-dimensional minimal surfaces }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 10 }, Pages = { 157-162 }, Year = { 1985 } } @Incollection{ Mic86, Author = { M.J. Micallef }, Title = { {S}table minimal surfaces in flat tori }, Booktitle = { {C}omplex differential geometry and non-linear differential equations }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 49 }, Pages = { 73-78 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Article{ MicMoo88, Author = { M.J. Micallef and J.D. Moore }, Title = { {M}inimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes }, Journal = { Ann.\ of Math. }, Volume = { 127 }, Pages = { 199-227 }, Year = { 1988 } } @Article{ MicWan93, Author = { M.J. Micallef and M.Y. Wang }, Title = { {M}etrics with non-negative isotropic curvature }, Journal = { Duke Math.\ J. }, Volume = { 72 }, Pages = { 649-672 }, Year = { 1993 } } @Article{ MicWhi87, Author = { M.J. Micallef and B. White }, Title = { {T}he structure of branch points in area minimizing surfaces and in pseudoholomorphic curves }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 12 }, Pages = { 117-123 }, Year = { 1987 } } @Article{ MicWhi94, Author = { M.J. Micallef and B. White }, Title = { {O}n the structure of branch points in minimal surfaces and in pseudoholomorphic curves }, Journal = { Ann.\ of Math. }, Volume = { 139 }, Pages = { 35-85 }, Year = { 1994 } } @Article{ MicWol93, Author = { M.J. Micallef and J.G. Wolfson }, Title = { {T}he second variation of area of minimal surfaces in four-manifolds }, Journal = { Math.\ Ann. }, Volume = { 295 }, Pages = { 245-267 }, Year = { 1993 } } @Misc{ MicB, Author = { M.-L. Michelsohn }, Title = { {S}urfaces minimales dans les sph\`eres } } @Article{ Mik94, Author = { M. Mikhail }, Title = { {P}artial regularity for harmonic maps of evolution into spheres }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 19 }, Pages = { 761-790 }, Year = { 1994 } } @Article{ MikZak78, Author = { A.V. Mikhailov and V.E. Zakharov }, Title = { {R}elativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method }, Journal = { Soviet Phys.\ JETP }, Volume = { 47 }, Pages = { 1017-1027 }, Year = { 1978 } } @Article{ Mik81, Author = { V.M. Mikljukov }, Title = { {A}symptotic properties of subsolutions of quasilinear equations of elliptic type and mappings with bounded dilatation }, Journal = { Math.\ USSR-Sb. }, Volume = { 39 }, Pages = { 37-60 }, Year = { 1981 } } @Article{ MilRos51, Author = { A. Milgram and P. Rosenbloom }, Title = { {H}armonic forms and heat conduction, {I} }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 37 }, Pages = { 180-184 }, Year = { 1951 } } @Misc{ Mil, Author = { T.K. Milnor }, Title = { {A}ssociate harmonic immersions and assigned timelike minimal surfaces } } @Unpublished{ MilA, Author = { T.K. Milnor }, Title = { {T}he energy {$1$} metric on harmonically immersed surfaces }, Note = { preprint } } @Misc{ MilB, Author = { T.K. Milnor }, Title = { {E}ntire timelike minimal surfaces in {${E}^3_1$} } } @Unpublished{ MilC, Author = { T.K. Milnor }, Title = { {H}armonic immersions of a surface with prescribed semi-{R}iemannian metric }, Note = { preprint } } @Article{ Mil77, Author = { T.K. Milnor }, Title = { {A} characterization of harmonic immersions of surfaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 83 }, Pages = { 403-405 }, Year = { 1977 } } @Article{ Mil79, Author = { T.K. Milnor }, Title = { {H}armonically immersed surfaces }, Journal = { J. Differential Geom. }, Volume = { 14 }, Pages = { 205-214 }, Year = { 1979 } } @Article{ Mil80, Author = { T.K. Milnor }, Title = { {A}bstract {W}eingarten surfaces }, Journal = { J. Differential Geom. }, Volume = { 15 }, Pages = { 365-380 }, Year = { 1980 } } @Article{ Mil80A, Author = { T.K. Milnor }, Title = { {M}apping surfaces harmonically into {${\bf {E}}^n$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 78 }, Pages = { 269-275 }, Year = { 1980 } } @Incollection{ Mil81, Author = { T.K. Milnor }, Title = { {C}lassifying harmonic immersions of a surface in {${E}^n$} }, Booktitle = { {C}ontrib. {A}nal. and {G}eo. {J}ohn {H}opkins }, Pages = { 211-218 }, Year = { 1981 } } @Article{ Mil82, Author = { T.K. Milnor }, Title = { {C}haracterizing harmonic immersions of surfaces with indefinite metric }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 79 }, Pages = { 2143-2144 }, Year = { 1982 } } @Incollection{ Mil83, Author = { T.K. Milnor }, Title = { {A}re harmonically immersed surfaces at all like minimally immersed surfaces? }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 99-110 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Article{ Mil83A, Author = { T.K. Milnor }, Title = { {H}armonic maps and classical surface theory in {M}inkowski {$3$}-space }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 280 }, Pages = { 161-185 }, Year = { 1983 } } @Incollection{ Mil85, Author = { T.K. Milnor }, Title = { {H}armonically immersed {L}orentz surfaces }, Booktitle = { {G}eo. {P}roc. }, Publisher = { World Scient.\ Publ. }, Pages = { 201-213 }, Year = { 1985 } } @Article{ Mil85A, Author = { T.K. Milnor }, Title = { {I}ntrinsic curvature of the induced metric on harmonically immersed surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 94 }, Pages = { 549-552 }, Year = { 1985 } } @Incollection{ Mil87, Author = { T.K. Milnor }, Title = { {A} conformal analog of {B}ernstein's theorem for timelike surfaces in {M}inkowski's {$3$}-space }, Booktitle = { {T}he legacy of {S}onya {K}owalevskaya }, Editor = { L. Keen }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 64 }, Pages = { 123-132 }, Series = { Contemp.\ Math. }, Year = { 1987 } } @Article{ Mil90, Author = { T.K. Milnor }, Title = { {A}ssociate harmonic immersions in {$3$}-space }, Journal = { Michigan Math.\ J. }, Volume = { 37 }, Pages = { 179-190 }, Year = { 1990 } } @Article{ Min84, Author = { Min-Oo }, Title = { {M}aps of minimum energy from compact simply-connected {L}ie groups }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 2 }, Pages = { 119-128 }, Year = { 1984 } } @Article{ Min92, Author = { Y.N. Minsky }, Title = { {H}armonic maps, length and energy in {T}eichm\"uller space }, Journal = { J. Differential Geom. }, Volume = { 35 }, Pages = { 151-217 }, Year = { 1992 } } @Article{ Min92A, Author = { Y.N. Minsky }, Title = { {H}armonic maps into hyperbolic {$3$}-manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 332 }, Pages = { 607-632 }, Year = { 1992 } } @Article{ Mir71, Author = { M. Miranda }, Title = { {F}rontiere minimali con ostacoli }, Journal = { Ann.\ Univ.\ Ferrara Sez.\ VII Sci.\ Mat. }, Volume = { 16 }, Pages = { 29-37 }, Year = { 1971 } } @Article{ Mir80, Author = { M. Miranda }, Title = { {T}he {D}irichlet problem for the minimal surface equation }, Journal = { Rend.\ Sem.\ Mat.\ Fis.\ Milano }, Volume = { 50 }, Pages = { 117-121 }, Note = { (Italian with English summary) }, Year = { 1980 } } @Article{ Mis78, Author = { C.W. Misner }, Title = { {H}armonic maps as models for physical theories }, Journal = { Phys.\ Rev.\ D }, Volume = { 18 }, Pages = { 4510-4524 }, Year = { 1978 } } @Article{ Mit70, Author = { J.C. Mitteau }, Title = { {S}ur le laplacien des applications }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 270 }, Pages = { 603-605 }, Year = { 1970 } } @Article{ Mit70A, Author = { J.C. Mitteau }, Title = { {S}ur les solutions de l'\'equation de la chaleur }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 270 }, Pages = { 1244-1247 }, Year = { 1970 } } @Article{ Mit70B, Author = { J.C. Mitteau }, Title = { {U}ne formule de {G}reen g\'en\'eralis\'ee }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 271 }, Pages = { 654-657 }, Year = { 1970 } } @Unpublished{ Mit71, Author = { J.C. Mitteau }, Title = { {L}'\'equation parabolique sur les applications de vari\'et\'es---{M}\'ethodes g\'eom\'etriques en analyse globale }, Note = { Univ. Paris VI Ph.D Thesis }, Year = { 1971 } } @Incollection{ Mit74, Author = { J.C. Mitteau }, Title = { {E}xistence des applications harmoniques }, Booktitle = { {G}\'eom\'etrie diff\'erentielle, {C}oll. {S}antiago di {C}ompostella 1972 }, Editor = { E. Vidal }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 392 }, Pages = { 90-96 }, Series = { Lecture Notes in Math. }, Year = { 1974 } } @Article{ Mit74A, Author = { J.C. Mitteau }, Title = { {S}ur les applications harmoniques }, Journal = { J. Differential Geom. }, Volume = { 9 }, Pages = { 41-54 }, Year = { 1974 } } @Article{ Mit76, Author = { J.C. Mitteau }, Title = { {A}pplications harmoniques stables }, Journal = { M\'em.\ Soc.\ Math.\ France }, Volume = { 46 }, Pages = { 29-39 }, Year = { 1976 } } @Article{ Mit76A, Author = { J.C. Mitteau }, Title = { {M}inimums locaux de l'\'energie (courbure positive) }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 282 }, Pages = { 471-474 }, Year = { 1976 } } @Incollection{ Mit76B, Author = { J.C. Mitteau }, Title = { {S}tability of isometries among harmonic mappings }, Booktitle = { {C}omplex {A}nalysis and its {A}pplications, {I}{I}{I} }, Publisher = { I.C.T.P. }, Address = { Trieste }, Pages = { 49-61 }, Year = { 1976 } } @Article{ Miy68, Author = { Y. Miyahara }, Title = { {O}n some properties of a {T}eichm\"uller mapping }, Journal = { TRU Math. }, Volume = { 4 }, Pages = { 36-43 }, Year = { 1968 } } @Article{ Miy69, Author = { Y. Miyahara }, Title = { {A} lemma on a family of harmonic mappings }, Journal = { TRU Math. }, Volume = { 5 }, Pages = { 5-8 }, Year = { 1969 } } @Article{ Miy69A, Author = { Y. Miyahara }, Title = { {A} remark on a {T}eichm\"uller mapping }, Journal = { TRU Math. }, Volume = { 5 }, Pages = { 1-3 }, Year = { 1969 } } @Article{ Miy69B, Author = { Y. Miyahara }, Title = { {A} theorem on a sequence of harmonic mappings }, Journal = { TRU Math. }, Volume = { 5 }, Pages = { 9-19 }, Year = { 1969 } } @Misc{ MiyNag, Author = { T. Miyano and J. Naguchi }, Title = { {M}oduli spaces and holomorphic mappings and {D}iaphantine geometry } } @Article{ Miy96, Author = { R. Miyaoka }, Title = { {T}he family of isometric superconformal harmonic maps and the affine {T}oda equations }, Journal = { J. Reine Angew.\ Math. }, Volume = { 481 }, Pages = { 1--25 }, Year = { 1996 } } @Article{ Miy94, Author = { Y. Miyata }, Title = { {F}inite type minimal {$2$}-spheres in a complex projective space }, Journal = { Tokyo J. Math. }, Volume = { 17 }, Pages = { 77-100 }, Year = { 1994 } } @Article{ Mo93, Author = { X.H. Mo }, Title = { {C}urvature pinching for compact minimal submanifolds in a sphere }, Journal = { J. Hangzhou Univ. }, Volume = { 20 }, Pages = { 251-255 }, Note = { (Chinese with English summary) }, Year = { 1993 } } @Incollection{ Mo93A, Author = { X.H. Mo }, Title = { {H}armonic maps from {R}iemann surface to complex {G}rassmannian }, Booktitle = { {D}ifferential {G}eometry ({S}hanghai, 1991) }, Publisher = { World Sci.\ Publishing }, Address = { River Edge, NJ }, Pages = { 159-169 }, Year = { 1993 } } @Article{ Mo93B, Author = { X.H. Mo }, Title = { {T}ournaments and almost complex structures on twistor spaces }, Journal = { J. Fudan Univ.\ Natur.\ Sci. }, Volume = { 32 }, Pages = { 46-51 }, Note = { (Chinese) }, Year = { 1993 } } @Article{ Mo94, Author = { X.H. Mo }, Title = { {T}he construction of harmonic maps from a {R}iemann surface to a complex {G}rassmann manifold }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 15 }, Pages = { 50-58 }, Note = { (Chinese) }, Year = { 1994 } } @Article{ Mo94A, Author = { X.H. Mo }, Title = { {C}onstruction of harmonic maps from {R}iemann surface to complex {G}rassmannian }, Journal = { Chinese J. Contemp.\ Math. }, Volume = { 15 }, Pages = { 65-75 }, Year = { 1994 } } @Article{ Mo94B, Author = { X.H. Mo }, Title = { {M}inimal surfaces with constant {K}{\"a}hler angle in complex projective spaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 121 }, Pages = { 569-571 }, Year = { 1994 } } @Article{ Mo95, Author = { X.H. Mo }, Title = { {A} characterization of harmonic surfaces in {${\bf {C}}{P}^n$} with constant {K}\"{a}hler angle }, Journal = { Beijing Daxue Xuebao }, Volume = { 31 }, Pages = { 277-281 }, Year = { 1995 } } @Article{ Mo95A, Author = { X.H. Mo }, Title = { {L}agrangian harmonic maps into {${\bf {C}}{P}^n$} }, Journal = { Sci.\ Sinica }, Volume = { 38 }, Pages = { 524-532 }, Year = { 1995 } } @Article{ Mo96, Author = { X.H. Mo }, Title = { {H}orizontally conformal maps and harmonic morphisms }, Journal = { Chinese J. Contemp.\ Math. }, Volume = { 17 }, Pages = { 245-252 }, Year = { 1996 } } @Article{ Mo96A, Author = { X.H. Mo }, Title = { {H}orizontally conformal maps and harmonic morphisms }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 17 }, Pages = { 443--450 }, Note = { (Chinese) }, Year = { 1996 } } @Article{ Mo96B, Author = { X.H. Mo }, Title = { {I}nclusive minimal surface in {${G}(2,n)$} }, Journal = { Beijing Daxue Xuebao }, Volume = { 32 }, Pages = { 271-275 }, Year = { 1996 } } @Article{ Mo96C, Author = { X.H. Mo }, Title = { {I}nclusive minimal surfaces in {${G}_{2,n}$} }, Journal = { Adv.\ in Math.\ (Beijing) }, Volume = { 25 }, Pages = { 257-262 }, Year = { 1996 } } @Article{ Mo96D, Author = { X.H. Mo }, Title = { {L}agrangian harmonic two-spheres in {${\bf {C}}{P}^n$} with few higher order singularities }, Journal = { Sci.\ Sinica }, Volume = { 39 }, Pages = { 583-588 }, Year = { 1996 } } @Article{ Mo96E, Author = { X.H. Mo }, Title = { {T}otally real minimal surfaces in complex {G}rassmannians }, Journal = { Chinese Sci.\ Bull. }, Volume = { 25 }, Pages = { 1163-1166 }, Year = { 1996 } } @Article{ Mo97, Author = { X.H. Mo }, Title = { {H}armonic two-spheres in {${\bf {C}}{P}^n$} with antipodal symmetry and complementation }, Journal = { Beijing Daxue Xuebao }, Volume = { 33 }, Pages = { 273-281 }, Year = { 1997 } } @Article{ Mo98, Author = { X.H. Mo }, Title = { {N}ew characterisation of pseudo-holomorphic curves in {${\bf {C}}{P}^n$} in terms of the {${A}_n$}-{T}oda equations }, Journal = { Beijing Daxue Xuebao }, Volume = { 34 }, Note = { (to appear) }, Year = { 1998 } } @Article{ Mo94C, Author = { X.K. Mo }, Title = { {V}alue distribution of the {G}auss map and the total curvature of complete minimal surfaces in {${\bf {R}}^n$} }, Journal = { Pacific J. Math. }, Volume = { 163 }, Pages = { 159-174 }, Year = { 1994 } } @Article{ MoOss90, Author = { X.K. Mo and R. Osserman }, Title = { {O}n the {G}auss map and total curvature of complete minimal surfaces and an extension of {F}ujimoto's theorem }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 343-355 }, Year = { 1990 } } @Incollection{ Mok84, Author = { N. Mok }, Title = { {A} survey of complete noncompact {K}\"ahler manifolds of positive curvature }, Booktitle = { {C}omplex {A}nalysis of {S}everal {V}ariables }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 41 }, Pages = { 151-162 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1984 } } @Article{ Mok85, Author = { N. Mok }, Title = { {T}he holomorphic or antiholomorphic character of harmonic maps into irreducible compact quotients of polydiscs }, Journal = { Math.\ Ann. }, Volume = { 272 }, Pages = { 197-216 }, Year = { 1985 } } @Article{ Mok88, Author = { N. Mok }, Title = { {S}trong rigidity of irreducible quotients of polydiscs of finite volume }, Journal = { Math.\ Ann. }, Volume = { 282 }, Pages = { 555-577 }, Year = { 1988 } } @Article{ Mok88A, Author = { N. Mok }, Title = { {T}he uniformisation theorem for compact {K}\"ahler manifolds of nonnegative holomorphic bisectional curvature }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 179-214 }, Year = { 1988 } } @Book{ Mok89, Author = { N. Mok }, Title = { {M}etric rigidity theorems on {H}ermitian locally symmetric manifolds }, Publisher = { World Sci. }, Address = { Singapore }, Volume = { 6 }, Series = { Ser.\ Pure Math. }, Year = { 1989 } } @Incollection{ Mok91, Author = { N. Mok }, Title = { {A}spects of {K}{\"a}hler geometry on arithmetic varieties }, Booktitle = { {S}everal complex variables and complex geometry }, Editor = { E. Bedford and J.P. D'Angelo and R.E. Greene and S.G. Krantz }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 52:2 }, Pages = { 335-396 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1991 } } @Article{ Mok92, Author = { N. Mok }, Title = { {F}actorization of semisimple discrete representations of {K}{\"a}hler groups }, Journal = { Invent.\ Math. }, Volume = { 110 }, Pages = { 557-614 }, Year = { 1992 } } @Article{ MokSiuYeu93, Author = { N. Mok and Y.T. Siu and S.K. Yeung }, Title = { {G}eometric superrigidity }, Journal = { Invent.\ Math. }, Volume = { 113 }, Pages = { 57-83 }, Year = { 1993 } } @Article{ MokZho86, Author = { N. Mok and J.Q. Zhong }, Title = { {C}urvature characterization of compact hermitian symmetric spaces }, Journal = { J. Differential Geom. }, Volume = { 23 }, Pages = { 15-67 }, Year = { 1986 } } @Unpublished{ Mon, Author = { S. Montaldo }, Title = { {O}n the stability of harmonic morphisms }, Note = { preprint } } @Article{ Mon96, Author = { S. Montaldo }, Title = { {$p$}-{H}armonic maps and stability of {R}iemannian submersions }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 10 }, Pages = { 537-550 }, Year = { 1996 } } @Unpublished{ Mon96A, Author = { S. Montaldo }, Title = { {S}tability of harmonic maps and morphisms }, Note = { Leeds PhD thesis }, Year = { 1996 } } @Misc{ MonRos, Author = { S. Montiel and A. Ros }, Title = { {I}ndex of complete minimal surfaces } } @Article{ MonRos86, Author = { S. Montiel and A. Ros }, Title = { {M}inimal immersions of surfaces by the first eigenvalues and conformal area }, Journal = { Invent.\ Math. }, Volume = { 83 }, Pages = { 153-166 }, Year = { 1986 } } @Incollection{ MonRos91, Author = { S. Montiel and A. Ros }, Title = { {S}chr\"odinger operators associated to holomorphic maps }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Editor = { D. Ferus and U. Pinkall and U. Simon and B. Wegner }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1481 }, Pages = { 147-179 }, Series = { Lecture Notes in Math. }, Year = { 1991 } } @Unpublished{ MonUrb94, Author = { S. Montiel and F. Urbano }, Title = { {S}econd variation of superminimal surfaces into self-dual {E}instein four-manifolds }, Note = { Preprint }, Year = { 1994 } } @Misc{ Moo, Author = { J.D. Moore }, Title = { {M}inimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-plans } } @Article{ Moo72, Author = { J.D. Moore }, Title = { {I}sometric immersions of space forms in space forms }, Journal = { Pacific J. Math. }, Volume = { 40 }, Pages = { 157-166 }, Year = { 1972 } } @Article{ Moo85, Author = { J.D. Moore }, Title = { {O}n the stability of minimal spheres and a two-dimensional version of {S}ynge's theorem }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 44 }, Pages = { 278-281 }, Year = { 1985 } } @Article{ Moo86, Author = { J.D. Moore }, Title = { {C}ompact {R}iemannian manifolds with positive curvature operator }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 14 }, Pages = { 279-282 }, Year = { 1986 } } @Article{ Moo90, Author = { J.D. Moore }, Title = { {O}n the number of minimal two-spheres of small area in manifolds with curvature bounded above }, Journal = { Math.\ Ann. }, Volume = { 288 }, Pages = { 323-343 }, Year = { 1990 } } @Article{ MooNor90, Author = { J.D. Moore and M.H. Noronha }, Title = { {I}sometric immersions with congruent {G}auss maps }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 110 }, Pages = { 463-469 }, Year = { 1990 } } @Article{ MooSch85, Author = { J.D. Moore and T. Schulte }, Title = { {M}inimal disks and compact hypersurfaces in {E}uclidean space }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 94 }, Pages = { 321-328 }, Year = { 1985 } } @Article{ Mor82, Author = { F. Morgan }, Title = { {O}n the singular structure of two-dimensional area-minizing surfaces in {${\bf {R}}^n$} }, Journal = { Math.\ Ann. }, Volume = { 261 }, Pages = { 101-110 }, Year = { 1982 } } @Article{ Mor85, Author = { F. Morgan }, Title = { {O}n finiteness of the number of stable minimal hypersurfaces with a fixed boundary }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 13 }, Pages = { 133-136 }, Year = { 1985 } } @Article{ Mor86, Author = { F. Morgan }, Title = { {O}n finiteness of the number of stable minimal hypersurfaces with a fixed boundary }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 35 }, Pages = { 779-833 }, Year = { 1986 } } @Misc{ Mor, Author = { H. Mori }, Title = { {S}table complete constant mean curvature surfacs in {${\bf {R}}^3$} and {${H}^3$} } } @Article{ Mor77, Author = { H. Mori }, Title = { {A} note on the stability of minimal surfaces in the {$3$}-dimensional unit sphere }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 26 }, Pages = { 977-980 }, Year = { 1977 } } @Article{ Mor77A, Author = { H. Mori }, Title = { {N}otes on the stability of minimal submanifolds of {R}iemannian manifolds }, Journal = { Yokohama Math.\ J. }, Volume = { 25 }, Pages = { 9-15 }, Year = { 1977 } } @Article{ Mor81, Author = { H. Mori }, Title = { {M}inimal surfaces of revolution in {${H}^3$} and their stability properties }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 30 }, Pages = { 787-794 }, Year = { 1981 } } @Article{ Mor81A, Author = { H. Mori }, Title = { {R}emarks on the paper of {B}arbosa and do~{C}armo }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 37 }, Pages = { 173-178 }, Year = { 1981 } } @Article{ Mor89, Author = { L. Mori }, Title = { {H}armonic maps with prescribed finite singularities }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 14 }, Pages = { 1509-1540 }, Year = { 1989 } } @Article{ Mor91, Author = { L. Mori }, Title = { {U}niqueness of energy minimizing maps for almost all smooth boundary data }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 40 }, Pages = { 363-392 }, Year = { 1991 } } @Article{ MorNoj86, Author = { T. Morozumi and S. Nojiri }, Title = { {A}n analysis of non-compact non-linear {$\sigma$} models }, Journal = { Progr.\ Theoret.\ Phys. }, Volume = { 75 }, Pages = { 677-685 }, Year = { 1986 } } @Article{ Mor48, Author = { C.B. Morrey }, Title = { {T}he problem of {P}lateau on a {R}iemannian manifold }, Journal = { Ann.\ of Math. }, Volume = { 49 }, Pages = { 807-851 }, Year = { 1948 } } @Book{ Mor66, Author = { C.B. Morrey }, Title = { {M}ultiple integrals in the calculus of variations }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 130 }, Series = { Grundlehren Math.\ Wiss. }, Year = { 1966 } } @Article{ Mor40, Author = { M. Morse }, Title = { {T}he first variation in minimal surface theory }, Journal = { Duke Math.\ J. }, Volume = { 6 }, Pages = { 263-289 }, Year = { 1940 } } @Article{ MorTom39, Author = { M. Morse and C.B. Tompkins }, Title = { {T}he existence of minimal surfaces of general critical types }, Journal = { Ann.\ of Math. }, Volume = { 40 }, Pages = { 443-472 }, Year = { 1939 } } @Article{ MorTom39A, Author = { M. Morse and C.B. Tompkins }, Title = { {T}he existence of minimal surfaces of higher topological types }, Journal = { Ann.\ of Math. }, Volume = { 40 }, Pages = { 443-472 }, Year = { 1939 } } @Article{ MorTom40, Author = { M. Morse and C.B. Tompkins }, Title = { {U}nstable minimal surfaces of higher topological types }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 26 }, Pages = { 713-716 }, Year = { 1940 } } @Article{ MorTom41, Author = { M. Morse and C.B. Tompkins }, Title = { {M}inimal surfaces not of minimum type by a new method of approximation }, Journal = { Ann.\ of Math. }, Volume = { 42 }, Pages = { 62-72 }, Year = { 1941 } } @Article{ MorTom41A, Author = { M. Morse and C.B. Tompkins }, Title = { {U}nstable minimal surfaces of higher topological structure }, Journal = { Duke Math.\ J. }, Volume = { 8 }, Pages = { 350-375 }, Year = { 1941 } } @Incollection{ Mor88, Author = { J.M. Morvan }, Title = { {S}ous-vari{\'e}t{\'e}s complexes et isotropes minimales de {${\bf {C}}^m$} et {${\bf {C}}{P}^m$}. {L}e point de vue riemannien }, Booktitle = { {A}ction hamiltoniennes de groupes. {T}roisi{\`e}me th{\'e}or{\`e}me de {L}ie ({L}yon 1986) }, Publisher = { Hermann }, Volume = { 27 }, Pages = { 129-140 }, Series = { Travaux en Cours }, Year = { 1988 } } @Article{ Mos61, Author = { J. Moser }, Title = { {O}n {H}arnack's theorem for elliptic differential equations }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 14 }, Pages = { 577-591 }, Year = { 1961 } } @Book{ Mos73, Author = { G.D. Mostow }, Title = { {S}trong rigidity of locally symmetric spaces }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 78 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1973 } } @Article{ MosSiu80, Author = { G.D. Mostow and Y.T. Siu }, Title = { {A} compact {K}\"ahler surface of negative curvature not covered by the ball }, Journal = { Ann.\ of Math. }, Volume = { 112 }, Pages = { 321-360 }, Year = { 1980 } } @Article{ Mot81, Author = { K. Motomiya }, Title = { {O}n functions which satisfy some differential inequalities on {R}iemannian manifolds }, Journal = { Nagoya Math.\ J. }, Volume = { 81 }, Pages = { 57-72 }, Year = { 1981 } } @Article{ Mou89, Author = { L.B. Mou }, Title = { {H}armonic maps with prescribed finite singularities }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 14 }, Pages = { 1509-1540 }, Year = { 1989 } } @Incollection{ Mou93, Author = { L.B. Mou }, Title = { {H}armonic maps for bumpy metrics }, Booktitle = { {S}tatistical thermodynamics and differential geometry of microstructured materials }, Publisher = { Springer }, Volume = { 51 }, Pages = { 57-68 }, Series = { IMA Vol.\ Math.\ Appl. }, Year = { 1993 } } @Article{ MouYan, Author = { L. Mou and P. Yang }, Title = { {R}egularity of {$n$}-harmonic maps }, Journal = { J. Geom.\ Anal. }, Note = { (to appear) } } @Article{ Muk93, Author = { M. Mukai }, Title = { {O}n the connectedness of the space of harmonic {$2$}-spheres in real {G}rassmann manifolds of {$2$}-planes }, Journal = { Natur.\ Sci.\ Rep.\ Ochanomizu Univ. }, Volume = { 44 }, Pages = { 99-115 }, Year = { 1993 } } @Article{ Muk94, Author = { M. Mukai }, Title = { {O}n the connectedness of the space of harmonic {$2$}-spheres in quaternionic projective spaces }, Journal = { Tokyo J. Math. }, Volume = { 17 }, Pages = { 241-252 }, Year = { 1994 } } @Article{ Mum71, Author = { D. Mumford }, Title = { {A} remark on {M}ahler's compactness theorem }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 28 }, Pages = { 289-294 }, Year = { 1971 } } @Incollection{ Mur92, Author = { S. Murakami }, Title = { {H}armonic connections and their applications }, Booktitle = { {P}roc. {M}anila {C}onf. }, Year = { 1992 } } @Misc{ Mus, Author = { R. Musina }, Title = { {${S}^2$}-type minimal surfaces enclosing many obstacles in {${\bf {R}}^3$} } } @Incollection{ Mus91, Author = { R. Musina }, Title = { {V}ariational problems with obstacles and harmonic maps }, Booktitle = { {N}ematics: {M}athematical and {P}hysical {A}spects }, Editor = { J.-M. Coron and J.-M. Ghidaglia and F. H{\'e}lein }, Publisher = { Kluwer }, Address = { Dordrecht }, Volume = { 332 }, Pages = { 279-296 }, Series = { NATO Adv.\ Sci.\ Inst.\ Ser.\ C: Math.\ Phys.\ Sci. }, Year = { 1991 } } @Article{ Mus94, Author = { R. Musina }, Title = { {L}ower bounds for the {$p$}-energy and a minimization property of the map {$x/\vert x\vert$} }, Journal = { Ricerche Mat. }, Volume = { 43 }, Pages = { 335-346 }, Year = { 1994 } } @Article{ Mus89, Author = { E. Musso }, Title = { {O}n the twistor space of the six-sphere }, Journal = { Bull.\ Austral.\ Math.\ Soc. }, Volume = { 39 }, Pages = { 119-127 }, Year = { 1989 } } @Misc{ MusNic, Author = { E. Musso and L. Nicolodi }, Title = { {A} variational problem for surfaces in {L}aguerre geometry } } @Misc{ MusA, Author = { M.T. Mustafa }, Title = { {A} {B}ochner technique for harmonic morphisms } } @Article{ Mut89, Author = { H. Muto }, Title = { {O}n the stability of a three-sphere }, Journal = { Kodai Math.\ J. }, Volume = { 12 }, Pages = { 109-115 }, Year = { 1989 } } @Article{ Mut93, Author = { H. Muto }, Title = { {I}sometry of {${S}^3(1)$} and isometric minimal immersions of {${S}^3(1)$} into {${S}^{4}$} }, Journal = { Tensor (N.S.) }, Volume = { 52 }, Pages = { 170-178 }, Year = { 1993 } } @Article{ MutOhnUra84, Author = { H. Muto and Y. Ohnita and H. Urakawa }, Title = { {H}omogeneous minimal hypersurfaces in the unit spheres and the first eigenvalues of their {L}aplacian }, Journal = { T\^ohoku Math.\ J. }, Volume = { 36 }, Pages = { 253-267 }, Year = { 1984 } } @Article{ Mut73, Author = { Y. Muto }, Title = { {S}ome critical mappings }, Journal = { T\^ohoku Math.\ J. }, Volume = { 25 }, Pages = { 487-498 }, Year = { 1973 } } @Article{ Mut75, Author = { Y. Muto }, Title = { {C}ritical {R}iemannian metrics }, Journal = { Tensor (N.S.) }, Volume = { 29 }, Pages = { 125-133 }, Year = { 1975 } } @Article{ Mut77, Author = { Y. Muto }, Title = { {R}iemannian submersions and critical {R}iemannian metrics }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 29 }, Pages = { 493-511 }, Year = { 1977 } } @Article{ Mut78, Author = { Y. Muto }, Title = { {T}he {G}auss map of a submanifold of a {E}uclidean space }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 30 }, Pages = { 85-100 }, Year = { 1978 } } @Article{ Mut83, Author = { Y. Muto }, Title = { {S}ome properties of isometric minimal immersions of spheres into spheres }, Journal = { Kodai Math.\ J. }, Volume = { 6 }, Pages = { 308-332 }, Year = { 1983 } } @Article{ Mut84, Author = { Y. Muto }, Title = { {I}sometric minimal immersions of spheres into spheres isotropic up to some order }, Journal = { Yokohama Math.\ J. }, Volume = { 32 }, Pages = { 159-180 }, Year = { 1984 } } @Article{ Mut84A, Author = { Y. Muto }, Title = { {S}ome properties of spherical harmonics }, Journal = { Yokohama Math.\ J. }, Volume = { 32 }, Pages = { 182-189 }, Year = { 1984 } } @Article{ Mut84B, Author = { Y. Muto }, Title = { {T}he space {${W}_2$} of isometric minimal immersions of the three dimensional sphere into spheres }, Journal = { Tokyo J. Math. }, Volume = { 7 }, Pages = { 337-358 }, Year = { 1984 } } @Article{ Mut86, Author = { Y. Muto }, Title = { {G}roups of motions and minimal immersions of spheres into spheres }, Journal = { Kodai Math.\ J. }, Volume = { 9 }, Pages = { 191-205 }, Year = { 1986 } } @Article{ Mut87, Author = { Y. Muto }, Title = { {S}ome isometric minimal immersions {${S}^3(1)\rightarrow {S}^{24}(r),\ r^2={1\over 8}$} which are not full }, Journal = { Tensor (N.S.) }, Volume = { 45 }, Pages = { 130-143 }, Year = { 1987 } } @Article{ Mun80, Author = { H.F. M{\"u}nzner }, Title = { {I}soparametrische {H}yperfl\"achen in {S}ph\"aren, {I} }, Journal = { Math.\ Ann. }, Volume = { 251 }, Pages = { 57-71 }, Year = { 1980 } } @Article{ Mun81, Author = { H.F. M{\"u}nzner }, Title = { {I}soparametrische {H}yperfl\"achen in {S}ph\"aren, {I}{I} }, Journal = { Math.\ Ann. }, Volume = { 256 }, Pages = { 215-232 }, Year = { 1981 } } @Article{ Nag91, Author = { S. Nag }, Title = { {S}elf-dual connections, hyperbolic metrics and harmonic mappings on {R}iemann surfaces }, Journal = { Proc.\ Indian Acad.\ Sci.\ Math.\ Sci. }, Volume = { 101 }, Pages = { 215-218 }, Year = { 1991 } } @Article{ Nag60, Author = { T. Nagano }, Title = { {O}n fibred {R}iemannian manifolds }, Journal = { Sci.\ Papers College Gen.\ Ed.\ Univ.\ Tokyo }, Volume = { 10 }, Pages = { 17-27 }, Year = { 1960 } } @Incollection{ Nag82, Author = { T. Nagano }, Title = { {S}tability of harmonic maps between symmetric spaces }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 130-137 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ NagSmy75, Author = { T. Nagano and B. Smyth }, Title = { {T}he {G}auss map of {K}aehler immersions }, Journal = { T\^ohoku Math.\ J. }, Volume = { 27 }, Pages = { 453-460 }, Year = { 1975 } } @Article{ NagSmy75A, Author = { T. Nagano and B. Smyth }, Title = { {M}inimal varieties and harmonic maps in tori }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 50 }, Pages = { 249-265 }, Year = { 1975 } } @Incollection{ NagSmy75B, Author = { T. Nagano and B. Smyth }, Title = { {M}inimal varieties in tori }, Booktitle = { {D}ifferential {G}eometry }, Editor = { S.S. Chern and R. Osserman }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 27 }, Pages = { 189-190 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1975 } } @Article{ NagSmy75C, Author = { T. Nagano and B. Smyth }, Title = { {S}ur les surfaces minimales hyperelliptiques dans un tore }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 280 }, Pages = { 1527-1529 }, Year = { 1975 } } @Article{ NagSmy76, Author = { T. Nagano and B. Smyth }, Title = { {M}inimal surfaces in tori by {W}eyl groups, {I} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 61 }, Pages = { 102-104 }, Year = { 1976 } } @Incollection{ NagSmy78, Author = { T. Nagano and B. Smyth }, Title = { {M}inimal surfaces in tori by {W}eyl groups, {I}{I} }, Booktitle = { {M}inimal submanifolds and geodesics }, Publisher = { Kaigai }, Address = { Tokyo }, Year = { 1978 } } @Article{ NagSmy78A, Author = { T. Nagano and B. Smyth }, Title = { {P}eriodic minimal surfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 53 }, Pages = { 29-55 }, Year = { 1978 } } @Article{ NagSmy80, Author = { T. Nagano and B. Smyth }, Title = { {H}armonic mappings and structures of manifolds }, Journal = { Mathematics }, Volume = { 1 }, Pages = { 533-555 }, Note = { (Japanese) }, Year = { 1980 } } @Article{ NagSmy80A, Author = { T. Nagano and B. Smyth }, Title = { {O}n the {N}eumann problem for the nonlinear parabolic equations of {E}ells--{S}ampson and harmonic maps }, Journal = { Math.\ Ann. }, Volume = { 249 }, Pages = { 177-190 }, Year = { 1980 } } @Article{ NagSmy80B, Author = { T. Nagano and B. Smyth }, Title = { {P}eriodic minimal surfaces and {W}eyl groups }, Journal = { Acta Math. }, Volume = { 145 }, Pages = { 1-27 }, Year = { 1980 } } @Article{ NagSmy81, Author = { T. Nagano and B. Smyth }, Title = { {O}n the existence of global solutions of the nonlinear parabolic equation of {E}ells--{S}ampson over product manifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 82 }, Pages = { 369-373 }, Year = { 1981 } } @Article{ NagSum92, Author = { T. Nagano and M. Sumi }, Title = { {S}tability of {$p$}-harmonic maps }, Journal = { Tokyo J. Math. }, Volume = { 15 }, Pages = { 475-482 }, Year = { 1992 } } @Article{ Nag95, Author = { T. Nagasawa }, Title = { {I}nitial value and final value problems related to equivariant harmonic maps. {I}{I}. }, Journal = { S{\^u}rikaisekikenky{\^u}sho K{\^o}ky{\^u}roku }, Volume = { 911 }, Pages = { 1--10 }, Note = { (Japanese) }, Year = { 1995 } } @Misc{ NagUen, Author = { T. Nagasawa and K. Ueno }, Title = { {I}nitial-final value problems for equivariant harmonic maps } } @Article{ Nag81, Author = { T. Nagura }, Title = { {O}n the {J}acobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres, {I} }, Journal = { Osaka J. Math. }, Volume = { 18 }, Pages = { 115-145 }, Year = { 1981 } } @Article{ Nag82A, Author = { T. Nagura }, Title = { {O}n the {J}acobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres, {I}{I}{I} }, Journal = { Osaka J. Math. }, Volume = { 19 }, Pages = { 241 }, Year = { 1982 } } @Article{ Nag82B, Author = { T. Nagura }, Title = { {O}n the {J}acobi differential operators associated to minimal isometric immersions of symmetric spaces into spheres, {I}{I} }, Journal = { Osaka J. Math. }, Volume = { 19 }, Pages = { 79-124 }, Year = { 1982 } } @Article{ Nag83, Author = { T. Nagura }, Title = { {O}n the normal bundles of {${S}^2$} minimally immersed in the unit spheres }, Journal = { Osaka J. Math. }, Volume = { 20 }, Pages = { 779-786 }, Year = { 1983 } } @Misc{ Nai, Author = { H. Naito }, Title = { {A}symptotic behavior of non-linear heat equations in geometric variational problems } } @Article{ Nai88, Author = { H. Naito }, Title = { {A} stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations. }, Journal = { Compositio Math. }, Volume = { 68 }, Pages = { 221-239 }, Year = { 1988 } } @Article{ Nai89, Author = { H. Naito }, Title = { {A}symptotic behavior of solutions to {E}ells--{S}ampson equation near stable harmonic maps }, Journal = { Math.\ Z. }, Volume = { 202 }, Pages = { 383-389 }, Year = { 1989 } } @Incollection{ Nai89A, Author = { H. Naito }, Title = { {O}n the holomorphicity of pluriharmonic maps }, Booktitle = { {G}eometry of manifolds }, Editor = { K. Shiohama }, Publisher = { Academic Press }, Address = { San Diego }, Volume = { 8 }, Pages = { 419-425 }, Series = { Perspect.\ Math. }, Year = { 1989 } } @Article{ Nai93, Author = { H. Naito }, Title = { {O}n a local {H}\"older continuity for a minimizer of the exponential energy functional }, Journal = { Nagoya Math.\ J. }, Volume = { 129 }, Pages = { 97-113 }, Year = { 1993 } } @Incollection{ Nai93A, Author = { H. Naito }, Title = { {R}ecent developments of the evolution of harmonic maps }, Booktitle = { {G}eo. and its {A}ppl. }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 175-193 }, Year = { 1993 } } @Article{ Nai81, Author = { H. Naitoh }, Title = { {I}sotropic submanifolds with paralled second fundamental form in {${P}^n({\bf {C}})$} }, Journal = { Osaka J. Math. }, Volume = { 18 }, Pages = { 427-464 }, Year = { 1981 } } @Article{ Nai81A, Author = { H. Naitoh }, Title = { {T}otally real parallel submanifolds in {${P}^n({\bf {C}})$} }, Journal = { Tokyo J. Math. }, Volume = { 4 }, Pages = { 279-306 }, Year = { 1981 } } @Article{ NakTak88, Author = { H. Nakagawa and R. Takagi }, Title = { {H}armonic foliations on a compact {R}iemannian manifold of non-negative constant curvature }, Journal = { T\^ohoku Math.\ J. }, Volume = { 40 }, Pages = { 465-471 }, Year = { 1988 } } @Misc{ Nak, Author = { N. Nakauchi }, Title = { {B}ehavior of solutions of the gradient flow equations for the {Y}amabe functional } } @Misc{ NakA, Author = { N. Nakauchi }, Title = { {C}oncentration or blowup in smooth solutions of semilinear heat equations } } @Misc{ NakB, Author = { N. Nakauchi }, Title = { {A} concentration phenomenon in mean curvature flow } } @Misc{ NakC, Author = { N. Nakauchi }, Title = { {A} semilinear elliptic differential inequality } } @Article{ Nak93, Author = { N. Nakauchi }, Title = { {H}omomorphism between homotopy group induced by elements of the {S}obolev spaces {${L}^{1,p}({M},{N})$} }, Journal = { Manuscripta Math. }, Volume = { 78 }, Pages = { 1-7 }, Year = { 1993 } } @Article{ Nak96, Author = { N. Nakauchi }, Title = { {R}egularity of minimizing {$p$}-harmonic maps into the sphere }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 10 }, Pages = { 143-156 }, Year = { 1996 } } @Article{ NakTak95, Author = { N. Nakauchi and S. Takakuwa }, Title = { {A} remark on {$p$}-harmonic maps }, Journal = { Nonlinear Anal. }, Volume = { 25 }, Pages = { 169-185 }, Year = { 1995 } } @Incollection{ Nan90, Author = { A. Nannicini }, Title = { {K}{\"a}hlerian twistor spaces }, Booktitle = { {C}onference on {A}nalytic {G}eometry and {C}omplex {A}nalysis }, Pages = { 25-38 }, Note = { (Italian) }, Year = { 1990 } } @Article{ Nan92, Author = { A. Nannicini }, Title = { {T}wistor methods in {K}{\"a}hler geometry }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 6 }, Pages = { 411-417 }, Year = { 1992 } } @Article{ Nan92A, Author = { A. Nannicini }, Title = { {V}anishing theorems for twistor spaces }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 19 }, Pages = { 183-205 }, Year = { 1992 } } @Article{ Nay90, Author = { S. Nayatani }, Title = { {L}ower bounds for the {M}orse index of complete minimal surfaces in {E}uclidean {$3$}-space }, Journal = { Osaka J. Math. }, Volume = { 27 }, Pages = { 453-464 }, Year = { 1990 } } @Article{ Nay93, Author = { S. Nayatani }, Title = { {M}orse index and {G}auss maps of complete minimal surfacs in {E}uclidean 3-space }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 68 }, Pages = { 511-537 }, Year = { 1993 } } @Unpublished{ Neg87, Author = { C.J.C. Negreiros }, Title = { {H}armonic maps from compact {R}iemann surfaces into flag manifolds }, Note = { Chicago Thesis }, Year = { 1987 } } @Article{ Neg88, Author = { C.J.C. Negreiros }, Title = { {S}ome remarks about harmonic maps into flag manifolds }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 37 }, Pages = { 617-636 }, Year = { 1988 } } @Article{ Neg90, Author = { C.J.C. Negreiros }, Title = { {E}quivariant harmonic maps into homogeneous spaces }, Journal = { J. Math.\ Phys. }, Volume = { 31 }, Pages = { 1635-1642 }, Year = { 1990 } } @Article{ Neg90A, Author = { C.J.C. Negreiros }, Title = { {H}armonic maps into periodic flag manifolds and into loop groups }, Journal = { J. Geom.\ Phys. }, Volume = { 7 }, Pages = { 339-361 }, Year = { 1990 } } @Article{ Neu86, Author = { G. Neugebauer }, Title = { {C}hiral fields as minimal surfaces }, Journal = { Wiss.\ Z. Friedrich-Schiller-Univ.\ Jena Natur.\ Reihe }, Volume = { 35 }, Pages = { 795-799 }, Year = { 1986 } } @Misc{ Neu, Author = { N. Neuss }, Title = { {A} {L}iouville theorem for harmonic maps and static {Y}ang--{M}ills fields } } @Article{ NicVan90, Author = { L. Nicolodi and L. Vanhecke }, Title = { {R}otations and {H}ermitian symmetric spaces }, Journal = { Monatsh.\ Math. }, Volume = { 109 }, Pages = { 279-291 }, Year = { 1990 } } @Article{ NicVan93, Author = { L. Nicolodi and L. Vanhecke }, Title = { {H}armonic and isometric rotations around a curve }, Journal = { Illinois J. Math. }, Volume = { 37 }, Pages = { 85-100 }, Year = { 1993 } } @Article{ NicVan93A, Author = { L. Nicolodi and L. Vanhecke }, Title = { {H}armonic and isometric rotations around a submanifold }, Journal = { Math.\ J. Okayama Univ. }, Volume = { 35 }, Pages = { 235-251 }, Year = { 1993 } } @Article{ Nie88, Author = { J. Nie }, Title = { {S}ome results of harmonic maps of manifolds }, Journal = { Math.\ Appl. }, Volume = { 1 }, Pages = { 23-27 }, Year = { 1988 } } @Unpublished{ Nie, Author = { B. Nielsen }, Title = { {A} theory of relativity incorporating a canonical representation of matter and {M}ach's principle by considering minimal immersions }, Note = { preprint } } @Misc{ Nie82, Author = { B. Nielsen }, Title = { {T}he stress-energy momentum tensor of the {G}auss map in the extended nonlinear {$\sigma$}-model }, Year = { 1982 } } @Article{ Nie87, Author = { B. Nielsen }, Title = { {M}inimal immersions, {E}instein's equations, and {M}ach's principle }, Journal = { J. Geom.\ Phys. }, Volume = { 4 }, Pages = { 1-20 }, Year = { 1987 } } @Incollection{ Nij58, Author = { A. Nijenhuis }, Title = { {G}eometric aspects of formal differential operations on tensor fields }, Booktitle = { {P}roc. {I}. {C}. {M}. }, Pages = { 463-469 }, Year = { 1958 } } @Unpublished{ Nis, Author = { S. Nishikawa }, Title = { {D}eformations of {R}iemannian metrics and manifolds with bounded curvature ratios }, Note = { preprint } } @Unpublished{ NisA, Author = { S. Nishikawa }, Title = { {O}n holomorphic equivalences of bounded domains in complete {K}\"ahler manifolds of negative curvature }, Note = { preprint } } @Article{ NisB, Author = { S. Nishikawa }, Title = { {O}n the existence of global solutions of the nonlinear parabolic equation of {E}ells--{S}ampson over product manifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. } } @Article{ Nis75, Author = { S. Nishikawa }, Title = { {T}he {G}auss map of {K}\"ahler immersions }, Journal = { T\^ohoku Math.\ J. }, Volume = { 27 }, Pages = { 453-460 }, Year = { 1975 } } @Article{ Nis80, Author = { S. Nishikawa }, Title = { {H}armonic mappings and structures of manifolds }, Journal = { Mathematics }, Volume = { 1 }, Pages = { 533-555 }, Note = { (In Japanese) }, Year = { 1980 } } @Article{ Nis80A, Author = { S. Nishikawa }, Title = { {O}n the {N}eumann problem for the nonlinear parabolic equation of {E}ells--{S}ampson and harmonic mappings }, Journal = { Math.\ Ann. }, Volume = { 249 }, Pages = { 177-190 }, Year = { 1980 } } @Article{ Nis84, Author = { S. Nishikawa }, Title = { {O}n maximal spacelike hpersurfaces in a {L}orentzian manifold }, Journal = { Nagoya Math.\ J. }, Volume = { 95 }, Pages = { 117-124 }, Year = { 1984 } } @Misc{ Nis94, Author = { S. Nishikawa }, Title = { {H}armonic maps of surfaces }, Volume = { 5 }, Pages = { 191-206 }, Series = { Proc.\ Top.\ Geo.\ Res.\ Center }, Year = { 1994 } } @Incollection{ NisOch80, Author = { S. Nishikawa and T. Ochiai }, Title = { {R}eports on harmonic maps and their applications }, Booktitle = { {S}urvey in geometry }, Note = { (Japanese) }, Year = { 1980 } } @Article{ NisShi83, Author = { S. Nishikawa and K. Shiga }, Title = { {O}n the holomorphic equivalence of bounded domains in complete {K}\"ahler manifolds of nonpositive curvature }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 35 }, Pages = { 273-278 }, Year = { 1983 } } @Article{ Nit58, Author = { J.C.C. Nitsche }, Title = { {O}n harmonic mappings }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 9 }, Pages = { 268-271 }, Year = { 1958 } } @Book{ Nit75, Author = { J.C.C. Nitsche }, Title = { {V}orlesungen \"uber {M}inimalfl\"achen }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 199 }, Series = { Grundlehren Math.\ Wiss. }, Year = { 1975 } } @Book{ Nit88, Author = { J.C.C. Nitsche }, Title = { {L}ectures on minimal surfaces, {V}ol. 1 }, Publisher = { Cambridge Univ.\ Press }, Address = { Cambridge }, Year = { 1988 } } @Article{ NitTak87, Author = { T. Nitta and M. Takeuchi }, Title = { {C}ontact structures on twistor spaces }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 39 }, Pages = { 139-162 }, Year = { 1987 } } @Article{ Nob, Author = { N. Nobumitsu }, Title = { {R}egularity of minimising {$p$}-harmonic maps into the sphere. }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 10 }, Pages = { 319-332 } } @Article{ NogSun82, Author = { J. Noguchi and T. Sunada }, Title = { {F}initeness of the family of rational and meromorphic mappings into algebraic varieties }, Journal = { Amer.\ J. Math. }, Volume = { 104 }, Pages = { 887-900 }, Year = { 1982 } } @Article{ Nom73, Author = { K. Nomizu }, Title = { {S}ome results in {E}. {C}artan's theory of isoparametric families of hypersurfaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 79 }, Pages = { 1184-1188 }, Year = { 1973 } } @Incollection{ Nom75, Author = { K. Nomizu }, Title = { {E}lie {C}artan's work on isoparametric families of hypersurfaces }, Booktitle = { {D}ifferential {G}eometry }, Editor = { S.S. Chern and R. Osserman }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 27 }, Pages = { 191-200 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1975 } } @Article{ NomSmy69, Author = { K. Nomizu and B. Smyth }, Title = { {A} formula of {S}imons' type and hypersurfaces with constant mean curvature }, Journal = { J. Differential Geom. }, Volume = { 3 }, Pages = { 367-377 }, Year = { 1969 } } @Article{ NomSmy69A, Author = { K. Nomizu and B. Smyth }, Title = { {O}n the {G}auss mapping for hypersurfaces of constant mean curvature in the sphere }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 44 }, Pages = { 484-490 }, Year = { 1969 } } @Article{ Nor87, Author = { T. Nore }, Title = { {S}econd fundamental form of a map }, Journal = { Ann.\ Mat.\ Pura Appl. }, Volume = { 146 }, Pages = { 281-310 }, Year = { 1987 } } @Article{ Nou72, Author = { O. Nouhaud }, Title = { {D}\'eformations infinit\'esimales harmoniques remarquables }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 275 }, Pages = { 1103-1105 }, Year = { 1972 } } @Article{ Nou72A, Author = { O. Nouhaud }, Title = { {T}ransformations infinit\'esimales harmoniques }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 274 }, Pages = { 573-576 }, Year = { 1972 } } @Article{ Nou73, Author = { O. Nouhaud }, Title = { {I}mmersion harmonique d'une vari\'et\'e riemannienne dans une tore }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 277 }, Pages = { 1065-1066 }, Year = { 1973 } } @Article{ Nou75, Author = { O. Nouhaud }, Title = { {A}pplications et d\'eformations projectives }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 280 }, Pages = { 1531-1534 }, Year = { 1975 } } @Article{ Nou77, Author = { O. Nouhaud }, Title = { {A}pplications harmoniques d'une vari\'et\'e riemannienne dans son fibr\'e tangent }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 284 }, Pages = { 815-818 }, Year = { 1977 } } @Article{ Nou77A, Author = { O. Nouhaud }, Title = { {A}pplications harmoniques dans un tore et vari\'et\'es homog\`enes }, Journal = { Rend.\ Mat. }, Volume = { 10 }, Pages = { 295-303 }, Year = { 1977 } } @Article{ Nou77B, Author = { O. Nouhaud }, Title = { {D}\'eformations infinit\'esimales harmoniques }, Journal = { Rend.\ Mat. }, Volume = { 10 }, Pages = { 87-108 }, Year = { 1977 } } @Article{ Nov83, Author = { S.P. Novikov }, Title = { {M}ultivalued functionals in modern mathematical physics }, Journal = { Atti Accad.\ Sci.\ Torino Cl.\ Sci.\ Fis.\ Mat.\ Natur. }, Volume = { 17 {\rm (Supplement)} }, Pages = { 635-644 }, Year = { 1983 } } @Article{ Nut74, Author = { Y. Nutku }, Title = { {G}eometry of dynamics in general relativity }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { A21 }, Pages = { 175-183 }, Year = { 1974 } } @Incollection{ Nut93, Author = { Y. Nutku }, Title = { {H}armonic map formulation of colliding electrovac plane waves }, Booktitle = { {D}irections in general relativity, vol. {I} }, Publisher = { C.U.P. }, Address = { Cambridge }, Pages = { 261-271 }, Year = { 1993 } } @Article{ OBrRaw85, Author = { N.R. O'Brian and J. Rawnsley }, Title = { {T}wistor spaces }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 3 }, Pages = { 29-58 }, Year = { 1985 } } @Article{ ONe66, Author = { B. O'Neill }, Title = { {T}he fundamental equations of a submersion }, Journal = { Michigan Math.\ J. }, Volume = { 13 }, Pages = { 459-469 }, Year = { 1966 } } @Article{ OSu74, Author = { J.J. O'Sullivan }, Title = { {M}anifolds without conjugate points }, Journal = { Math.\ Ann. }, Volume = { 210 }, Pages = { 295-311 }, Year = { 1974 } } @Article{ OSu76, Author = { J.J. O'Sullivan }, Title = { {R}iemannian manifolds without foral points }, Journal = { J. Differential Geom. }, Volume = { 11 }, Pages = { 321-333 }, Year = { 1976 } } @Article{ Oba68, Author = { M. Obata }, Title = { {T}he {G}auss map of immersions of {R}iemannian manifolds in spaces of constant curvature }, Journal = { J. Differential Geom. }, Volume = { 2 }, Pages = { 217-223 }, Year = { 1968 } } @Article{ OdyRyd95, Author = { M.S. Ody and L.H. Ryder }, Title = { {T}ime-independent solutions to the two-dimensional non-linear {${O}(3)$} sigma model and surfaces of constant mean curvature }, Journal = { Internat.\ J. Modern Phys.\ A }, Volume = { 10 }, Pages = { 337-364 }, Year = { 1995 } } @Article{ Oga85, Author = { T. Ogata }, Title = { {M}inimal surfaces in a sphere with {G}aussian curvature not less than {$1/6$} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 37 }, Pages = { 553-560 }, Year = { 1985 } } @Article{ Oga87, Author = { T. Ogata }, Title = { {U}.~{S}imon's conjecture on minimal surfaces in a sphere }, Journal = { Bull.\ Yamagata Univ.\ Natur.\ Sci. }, Volume = { 11 }, Pages = { 345-350 }, Year = { 1987 } } @Article{ Oga91, Author = { T. Ogata }, Title = { {C}urvature pinching theorem for minimal surfaces with constant {K}aehler angle in complex projective spaces }, Journal = { T\^ohoku Math.\ J. }, Volume = { 43 }, Pages = { 361-374 }, Year = { 1991 } } @Article{ Oga93, Author = { T. Ogata }, Title = { {C}urvature pinching theorem for minimal surfaces with constant {K}aehler angle in complex projective spaces. {I}{I} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 45 }, Pages = { 271-283 }, Year = { 1993 } } @Article{ Oh90, Author = { Y.G. Oh }, Title = { {S}econd variation and stabilities of minimal {L}agrangian submanifolds in {K}{\"a}hler manifolds }, Journal = { Invent.\ Math. }, Volume = { 101 }, Pages = { 501-519 }, Year = { 1990 } } @Misc{ Ohn, Author = { Y. Ohnita }, Title = { {O}n instability of harmonic foliations } } @Incollection{ Ohn84, Author = { Y. Ohnita }, Title = { {T}he first standard minimal immersions of compact irreducible symmetric spaces }, Booktitle = { {D}ifferential {G}eometry of {S}ubmanifolds }, Editor = { K. Kenmotsu }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1090 }, Pages = { 37-49 }, Series = { Lecture Notes in Math. }, Year = { 1984 } } @Article{ Ohn86, Author = { Y. Ohnita }, Title = { {S}tability of harmonic maps and standard minimal immersions }, Journal = { T\^ohoku Math.\ J. }, Volume = { 38 }, Pages = { 259-267 }, Year = { 1986 } } @Article{ Ohn86A, Author = { Y. Ohnita }, Title = { {S}table minimal submanifolds in compact rank one symmetric spaces }, Journal = { T\^ohoku Math.\ J. }, Volume = { 38 }, Pages = { 199-217 }, Year = { 1986 } } @Article{ Ohn86B, Author = { Y. Ohnita }, Title = { {T}otally real submanifolds with nonnegative sectional curvature }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 97 }, Pages = { 474-478 }, Year = { 1986 } } @Article{ Ohn87, Author = { Y. Ohnita }, Title = { {O}n pluriharmonicity of stable harmonic maps }, Journal = { J. London Math.\ Soc. }, Volume = { 35 }, Pages = { 563-568 }, Year = { 1987 } } @Article{ Ohn87A, Author = { Y. Ohnita }, Title = { {O}n stability of minimal submanifolds in compact symmetric spaces }, Journal = { Compositio Math. }, Volume = { 64 }, Pages = { 157-189 }, Year = { 1987 } } @Article{ Ohn89, Author = { Y. Ohnita }, Title = { {M}inimal surfaces with constant curvature and {K}\"ahler angle in complex space forms }, Journal = { Tsukuba J. Math. }, Volume = { 13 }, Pages = { 191-207 }, Year = { 1989 } } @Article{ Ohn90, Author = { Y. Ohnita }, Title = { {H}omogeneous harmonic maps into complex projective spaces }, Journal = { Tokyo J. Math. }, Volume = { 13 }, Pages = { 87-116 }, Year = { 1990 } } @Article{ Ohn93, Author = { Y. Ohnita }, Title = { {L}oop group actions on harmonic maps and {M}orse-{B}ott theory }, Journal = { S{\^u}rikaisekikenky{\^u}sho K{\^o}ky{\^u}roku }, Volume = { 822 }, Pages = { 110-122 }, Note = { (Japanese) }, Year = { 1993 } } @Incollection{ Ohn93A, Author = { Y. Ohnita }, Title = { {O}n deformations of harmonic 2-spheres in symmetric spaces }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 359-368 }, Year = { 1993 } } @Article{ Ohn94, Author = { Y. Ohnita }, Title = { {G}roup actions and deformations for harmonic maps into symmetric spaces }, Journal = { Kodai Math.\ J. }, Volume = { 17 }, Pages = { 463-475 }, Year = { 1994 } } @Article{ OhnTas86, Author = { Y. Ohnita and H. Tasaki }, Title = { {U}niqueness of certain {$3$}-dimensional, homologically volume minimizing submanifolds in compact simple {L}ie groups }, Journal = { Tsukuba J. Math. }, Volume = { 10 }, Pages = { 11-16 }, Year = { 1986 } } @Article{ OhnUda87, Author = { Y. Ohnita and S. Udagawa }, Title = { {S}table harmonic maps from {R}iemann surfaces to compact {H}ermitian symmetric spaces }, Journal = { Tokyo J. Math. }, Volume = { 10 }, Pages = { 385-390 }, Year = { 1987 } } @Article{ OhnUda90, Author = { Y. Ohnita and S. Udagawa }, Title = { {S}tability, complex-analyticity, and constancy of pluriharmonic maps from compact {K}\"ahler manifolds }, Journal = { Math.\ Z. }, Volume = { 205 }, Pages = { 624-644 }, Year = { 1990 } } @Incollection{ OhnUda91, Author = { Y. Ohnita and S. Udagawa }, Title = { {C}omplex-analyticity of pluriharmonic maps and their constructions }, Booktitle = { {P}rospects in {C}omplex {G}eometry }, Editor = { J. Noguchi and T. Ohsawa }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1468 }, Pages = { 371-407 }, Series = { Lecture Notes in Math. }, Year = { 1991 } } @Misc{ OhnVal, Author = { Y. Ohnita and G. Valli }, Title = { {F}actorization of weakly pluriharmonic maps by {H}arder--{N}arasimhan filtration } } @Article{ OhnVal90, Author = { Y. Ohnita and G. Valli }, Title = { {P}luriharmonic maps into compact {L}ie groups and factorization into unitons }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 61 }, Pages = { 546-570 }, Year = { 1990 } } @Article{ Oht91, Author = { H. Ohta }, Title = { {O}n harmonic maps from {${C}{P}^1$} to {$\{O}mega {S}{U}(n)$} }, Journal = { Sci.\ Papers College Arts Sci.\ Univ.\ Tokyo }, Volume = { 41 }, Pages = { 83-93 }, Year = { 1991 } } @Article{ Oka88, Author = { T. Okayasu }, Title = { {P}inching and nonexistence of stable harmonic maps }, Journal = { T\^ohoku Math.\ J. }, Volume = { 40 }, Pages = { 213-220 }, Year = { 1988 } } @Incollection{ Oka89, Author = { T. Okayasu }, Title = { {O}n the instability of minimal submanifolds and harmonic maps }, Booktitle = { {G}eometry of manifolds }, Editor = { K. Shiohama }, Publisher = { Acad.\ Press }, Address = { San Diego }, Volume = { 8 }, Pages = { 427-434 }, Series = { Perspect.\ Math. }, Year = { 1989 } } @Article{ Oka89A, Author = { T. Okayasu }, Title = { {O}n the instability of minimal submanifolds in {R}iemannian manifolds of positive curvature }, Journal = { Math.\ Z. }, Volume = { 201 }, Pages = { 33-44 }, Year = { 1989 } } @Article{ Oka91, Author = { T. Okayasu }, Title = { {I}solation phenomena for harmonic maps }, Journal = { Math.\ J. Toyama Univ. }, Volume = { 14 }, Pages = { 185-192 }, Year = { 1991 } } @Incollection{ Oka93, Author = { T. Okayasu }, Title = { {A}rea of minimal disks with free boundary }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 447-449 }, Year = { 1993 } } @Article{ Oka94, Author = { T. Okayasu }, Title = { {R}egularity of minimizing harmonic maps into {${S}^4$}, {${S}^5$} and symmetric spaces }, Journal = { Math.\ Ann. }, Volume = { 298 }, Pages = { 193-205 }, Year = { 1994 } } @Unpublished{ Olm92, Author = { C. Olmos }, Title = { {H}omogeneous submanifolds of higher rank and parallel mean curvature }, Note = { Augsburg preprint }, Year = { 1992 } } @Unpublished{ OmePer, Author = { C. Omero and R. Percacci }, Title = { {G}eneralized nonlinear {$\sigma$}-models in curved space and spontaneous compactification }, Note = { preprint } } @Article{ Omo67, Author = { H. Omori }, Title = { {I}sometric immersions of {R}iemannian manifolds }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 19 }, Pages = { 205-214 }, Year = { 1967 } } @Article{ Ono88, Author = { K. Ono }, Title = { {O}n the holomorphicity of harmonic maps from compact {K}\"ahler manifolds to hyperbolic {R}iemann surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 102 }, Pages = { 1071-1076 }, Year = { 1988 } } @Book{ Ono94, Author = { T. Ono }, Title = { {V}ariations on a theme of {E}uler }, Publisher = { Plenum Press }, Address = { New York }, Series = { Univ.\ Ser.\ Math. }, Year = { 1994 } } @Article{ Opr89, Author = { V. Oproiu }, Title = { {H}armonic maps between tangent bundles }, Journal = { Rend.\ Sem.\ Mat.\ Univ.\ Politec.\ Torino }, Volume = { 47 }, Pages = { 47-55 }, Year = { 1989 } } @Article{ Opr89A, Author = { V. Oproiu }, Title = { {O}n the harmonic sections of cotangent bundles }, Journal = { Rend.\ Sem.\ Fac.\ Sci.\ Univ.\ Cagliari }, Volume = { 59 }, Pages = { 177-184 }, Year = { 1989 } } @Article{ OrnRom93, Author = { L. Ornea and G. Romani }, Title = { {T}he fundamental equations of conformal submersions }, Journal = { Beitr{\"a}ge Algebra Geom. }, Volume = { 34 }, Pages = { 233-243 }, Year = { 1993 } } @Article{ Oss61, Author = { R. Osserman }, Title = { {M}inimal surfaces in the large }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 35 }, Pages = { 65-76 }, Year = { 1961 } } @Article{ Oss64, Author = { R. Osserman }, Title = { {G}lobal properties of minimal surfaces in {${E}^3$} and {${E}^n$} }, Journal = { Ann.\ of Math. }, Volume = { 80 }, Pages = { 340-364 }, Year = { 1964 } } @Article{ Oss69, Author = { R. Osserman }, Title = { {M}inimal varieties }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 75 }, Pages = { 1092-1120 }, Year = { 1969 } } @Book{ Oss69A, Author = { R. Osserman }, Title = { {A} survey of minimal surfaces }, Publisher = { Van Nostrand }, Volume = { 25 }, Series = { Van Nostrand Math.\ Studies }, Year = { 1969 } } @Article{ Oss70, Author = { R. Osserman }, Title = { {A} proof of the regularity everywhere of the classical solution to {P}lateau's problem }, Journal = { Ann.\ of Math. }, Volume = { 91 }, Pages = { 550-569 }, Year = { 1970 } } @Incollection{ Oss70A, Author = { R. Osserman }, Title = { {S}ome properties of solutions to the minimal surface system for arbitrary codimension }, Booktitle = { {G}lobal {A}nalysis, {P}art {I}{I} }, Editor = { S.S. Chern and S. Smale }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 15 }, Pages = { 283-291 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1970 } } @Article{ Oss72, Author = { R. Osserman }, Title = { {B}ranched immersions of surfaces }, Journal = { INDAM Symp.\ Math. }, Volume = { 10 }, Pages = { 141-158 }, Year = { 1972 } } @Article{ Oss73, Author = { R. Osserman }, Title = { {O}n {B}ers' theorem on isolated singularities }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 23 }, Pages = { 337-342 }, Year = { 1973 } } @Article{ Oss78, Author = { R. Osserman }, Title = { {T}he isoperimetric inequality }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 84 }, Pages = { 1182-1238 }, Year = { 1978 } } @Incollection{ Oss78A, Author = { R. Osserman }, Title = { {P}roperties of solutions to the minimal surface equation in higher codimension }, Booktitle = { {J}apan--{U}.{S}. {S}eminar on {M}inimal {S}ubmanifolds. {T}okyo }, Pages = { 163-172 }, Year = { 1978 } } @Incollection{ Oss80, Author = { R. Osserman }, Title = { {M}inimal surfaces, {G}auss maps, {T}otal curvature, {E}igenvalue estimates and stability }, Booktitle = { {T}he {C}hern {S}ymposium 1979 }, Editor = { W.Y. Hsiang and S. Kobayashi and I.M. Singer and A. Weinstein and J.A. Wolf and H.H. Wu }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Pages = { 199-227 }, Year = { 1980 } } @Incollection{ Oss84, Author = { R. Osserman }, Title = { {T}he minimal surface equation }, Booktitle = { {S}eminar on nonlinear partial differential equations }, Editor = { S.S. Chern }, Publisher = { Springer }, Address = { Berlin }, Volume = { 2 }, Pages = { 237-259 }, Series = { MSRI Publ. }, Year = { 1984 } } @Article{ OswPau88, Author = { L. Oswald and G. Paulik }, Title = { {A}n example of nonhomotopic solutions to the {D}irichlet problem for harmonic maps in two dimensions }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 104 }, Pages = { 1267-1270 }, Year = { 1988 } } @Article{ Ots70, Author = { T. Otsuki }, Title = { {M}inimal hypersurfaces in a {R}iemannian manifold of constant curvature }, Journal = { Amer.\ J. Math. }, Volume = { 92 }, Pages = { 145-173 }, Year = { 1970 } } @Incollection{ Ots72, Author = { T. Otsuki }, Title = { {O}n a {$2$}-dimensional {R}iemannian manifold }, Booktitle = { {D}iff. geo. in honor of {K}. {Y}ano. }, Publisher = { Kinokuniya }, Pages = { 401-414 }, Year = { 1972 } } @Article{ Ott85, Author = { S.K. Ottarsson }, Title = { {C}losed geodesics on {R}iemannian manifolds via the heat flow }, Journal = { J. Geom.\ Phys. }, Volume = { 2 }, Pages = { 49-72 }, Year = { 1985 } } @Incollection{ Otw92, Author = { T.H. Otway }, Title = { {R}emovable singularities of stationary fields }, Booktitle = { {T}he {P}roblem of {P}lateau }, Editor = { T.M. Rassias }, Publisher = { World Scientific }, Address = { River Edge, NJ }, Year = { 1992 } } @Unpublished{ Ou95, Author = { Y. Ou }, Title = { {C}omplete lifts of maps and harmonic morphisms between {E}uclidean spaces }, Note = { Preprint }, Year = { 1995 } } @Misc{ Ou, Author = { Y.L. Ou }, Title = { {C}omplete lifts of maps and harmonic morphisms between {E}uclidean spaces } } @Misc{ OuA, Author = { Y.L. Ou }, Title = { {Q}uadratic harmonic morphisms and 0-systems } } @Misc{ OuWoo, Author = { Y.L. Ou and J.C. Wood }, Title = { {O}n the classification of quadratic harmonic morphisms between {E}uclidean spaces } } @Article{ OzeTak75, Author = { H. Ozeki and M. Takeuchi }, Title = { {O}n some types of isoparametric hypersurfaces in spheres, {I} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 27 }, Pages = { 515-559 }, Year = { 1975 } } @Article{ OzeTak76, Author = { H. Ozeki and M. Takeuchi }, Title = { {O}n some types of isoparametric hypersurfaces in spheres, {I}{I} }, Journal = { T\^ohoku Math.\ J. }, Volume = { 28 }, Pages = { 7-55 }, Year = { 1976 } } @Misc{ Pab, Author = { H. Pabel }, Title = { {M}inimalfla{\"a}chen und die komplexe {\"{A}}hlichkeitsgruppe } } @Incollection{ Pab88, Author = { H. Pabel }, Title = { {Z}ur {K}lassifikation {E}uklidischer {M}inimalfl{\"a}chen }, Booktitle = { {P}roc. of the congress of geometry ({T}hessaloniki 1987) }, Publisher = { Aristotle Univ. }, Address = { Thessaloniki }, Pages = { 114-130 }, Year = { 1988 } } @Article{ Pal79, Author = { R.S. Palais }, Title = { {T}he principle of symmetric criticality }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 69 }, Pages = { 19-30 }, Year = { 1979 } } @Incollection{ Pal84, Author = { R.S. Palais }, Title = { {A}pplications of the symmetric criticality principle in mathematical physics and differential geometry }, Booktitle = { {P}roc. {S}econd {C}onference {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei 1981 }, Publisher = { Sci.\ Press }, Address = { Beijing }, Pages = { 247-301 }, Year = { 1984 } } @Article{ PalTer86, Author = { R.S. Palais and C.L. Terng }, Title = { {R}eduction of variables for minimal submanifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 98 }, Pages = { 480-484 }, Year = { 1986 } } @Book{ PalTer88, Author = { R.S. Palais and C.L. Terng }, Title = { {C}ritical point theory and submanifold geometry }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1353 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Misc{ Pal, Author = { B. Palmer }, Title = { {M}inimal surfaces and {${H}$}-surfaces with prescribed curvature } } @Unpublished{ PalA, Author = { B. Palmer }, Title = { {R}emarks on minimal tori in {${S}^3$} }, Note = { preprint } } @Misc{ PalB, Author = { B. Palmer }, Title = { {S}econd variation formulas for {W}ilmore surfaces } } @Misc{ PalC, Author = { B. Palmer }, Title = { {S}urfaces in {${H}^3_1$} } } @Article{ Pal88, Author = { B. Palmer }, Title = { {I}sothermic surfaces and the {G}auss map }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 104 }, Pages = { 876-884 }, Year = { 1988 } } @Article{ Pal90, Author = { B. Palmer }, Title = { {T}he {G}auss map of spacelike constant mean curvature }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 65 }, Pages = { 52-57 }, Year = { 1990 } } @Article{ Pal90A, Author = { B. Palmer }, Title = { {S}pacelike constant mean curvature surfaces in {P}seudo-{R}iemannian space forms }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 8 }, Pages = { 217-226 }, Year = { 1990 } } @Article{ Pal91, Author = { B. Palmer }, Title = { {I}ndex and stability of harmonic {G}auss maps }, Journal = { Math.\ Z. }, Volume = { 206 }, Pages = { 563-566 }, Year = { 1991 } } @Article{ Pal93, Author = { B. Palmer }, Title = { {M}inimal surfaces and {${H}$}-surfaces in non-positively curved space forms }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 119 }, Pages = { 245-250 }, Year = { 1993 } } @Incollection{ Pal93A, Author = { B. Palmer }, Title = { {S}tability of harmonic {G}auss maps }, Booktitle = { {G}eometry and topology of submanifolds, {V} }, Publisher = { World Sci.\ Publishing }, Address = { River Edge, NJ }, Pages = { 233-241 }, Year = { 1993 } } @Article{ Pan81, Author = { J.S. Pan }, Title = { {A}nti-quaternionic submanifolds of a quaternionic projective space }, Journal = { Kyungpook Math.\ J. }, Volume = { 21 }, Pages = { 91-115 }, Year = { 1981 } } @Unpublished{ Pan, Author = { Y.L. Pan }, Title = { {S}table harmonic maps and topology of submanifolds in {E}uclidean space }, Note = { preprint } } @Article{ Pan82, Author = { Y.L. Pan }, Title = { {S}ome nonexistence theorems for stable harmonic mappings }, Journal = { Chinese Ann.\ Math. }, Volume = { 3 }, Pages = { 515-518 }, Year = { 1982 } } @Article{ Pan83, Author = { Y.L. Pan }, Title = { {S}ubmanifolds with parallel mean curvature and {G}auss maps }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 4 }, Pages = { 171-176 }, Year = { 1983 } } @Incollection{ Pan84, Author = { Y.L. Pan }, Title = { {S}ome nonexistence theorems for stable harmonic mappings }, Booktitle = { {P}roc. {S}econd {C}onference {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei 1981 }, Publisher = { Sci.\ Press }, Address = { Beijing }, Pages = { 303-306 }, Year = { 1984 } } @Article{ Pan85, Author = { Y.L. Pan }, Title = { {P}inching theorems of {S}imons type for complete minimal submanifolds in the sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 93 }, Pages = { 710-712 }, Year = { 1985 } } @Article{ Pan89, Author = { Y.L. Pan }, Title = { {N}onexistence of stable harmonic maps from sufficiently pinched simply connected {R}iemannian manifolds }, Journal = { J. London Math.\ Soc. }, Volume = { 39 }, Pages = { 568-576 }, Year = { 1989 } } @Unpublished{ PanShe, Author = { Y.L. Pan and Y.B. Shen }, Title = { {S}table harmonic maps from submanifolds in space form }, Note = { preprint } } @Article{ PanShe85, Author = { Y.L. Pan and Y.B. Shen }, Title = { {O}n harmonic maps with finite energy }, Journal = { Acta Math.\ Sinica }, Volume = { 1 }, Pages = { 308-313 }, Year = { 1985 } } @Article{ PanShe85A, Author = { Y.L. Pan and Y.B. Shen }, Title = { {S}tability of harmonic maps and minimal immersions }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 93 }, Pages = { 111-117 }, Year = { 1985 } } @Article{ PanShe86, Author = { Y.L. Pan and Y.B. Shen }, Title = { {S}tability of harmonic maps from a {R}iemannian manifold with boundary }, Journal = { Kexue Tongbao (Chinese) }, Volume = { 31 }, Pages = { 170-173 }, Year = { 1986 } } @Incollection{ PanShe87, Author = { Y.L. Pan and Y.B. Shen }, Title = { {S}ome stability results of harmonic maps from a {R}iemannian manifold with boundary }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations }, Editor = { C.H. Gu and M. Berger and R. Bryant }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1255 }, Pages = { 80-87 }, Series = { Lecture Notes in Math. }, Year = { 1987 } } @Article{ PanShe90, Author = { Y.L. Pan and Y.B. Shen }, Title = { {S}table harmonic maps from pinched manifolds }, Journal = { Math.\ Z. }, Volume = { 203 }, Pages = { 493-501 }, Year = { 1990 } } @Article{ PanZha96, Author = { Y.L. Pan and D. Zhao }, Title = { {L}iouville-type theorems for harmonic maps }, Journal = { Chinese Ann.\ Math.\ Ser.\ A }, Volume = { 17 }, Pages = { 255--258 }, Note = { (Chinese) }, Year = { 1996 } } @Article{ Par93, Author = { G.H. Park }, Title = { {A} monotonicity inequality for unit vector fields }, Journal = { Honam.\ Math.\ J. }, Volume = { 15 }, Pages = { 11-16 }, Year = { 1993 } } @Article{ Par88, Author = { J.S. Park }, Title = { {H}olomorphic and harmonic maps between complete almost {K}\"ahler manifolds }, Journal = { Proc.\ Japan Acad.\ Ser.\ A Math.\ Sci. }, Volume = { 64 }, Pages = { 389-392 }, Year = { 1988 } } @Article{ Par90, Author = { J.S. Park }, Title = { {H}armonic inner automorphisms of compact connected semisimple {L}ie groups }, Journal = { T\^ohoku Math.\ J. }, Volume = { 42 }, Pages = { 83-91 }, Year = { 1990 } } @Article{ ParUra91, Author = { J.S. Park and H. Urakawa }, Title = { {C}lassification of harmonic mappings of constant energy density into spheres }, Journal = { Geom.\ Dedicata }, Volume = { 37 }, Pages = { 211-226 }, Year = { 1991 } } @Unpublished{ Par, Author = { K.S. Park }, Title = { {I}soparametric families in projective spaces }, Note = { preprint } } @Article{ Par83, Author = { M. Parker }, Title = { {O}rthogonal multiplications in small dimensions }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 15 }, Pages = { 368-372 }, Year = { 1983 } } @Article{ Par84, Author = { T. Parker }, Title = { {C}onformal fields and stability }, Journal = { Math.\ Z. }, Volume = { 185 }, Pages = { 305-319 }, Year = { 1984 } } @Article{ ParWol93, Author = { T.H. Parker and J.G. Wolfson }, Title = { {P}seudo-holomorphic maps and bubbletrees }, Journal = { J. Geom.\ Anal. }, Volume = { 3 }, Pages = { 63-98 }, Year = { 1993 } } @Misc{ ParA, Author = { V.K. Parmar }, Title = { {H}armonic morphisms between semi-{R}iemannian manifolds } } @Unpublished{ Par91, Author = { V.K. Parmar }, Title = { {H}armonic morphisms between semi-{R}iemannian manifolds }, Note = { Leeds Thesis }, Year = { 1991 } } @Article{ ParPol83, Author = { W. Parry and M. Pollicott }, Title = { {A}n analogue of the prime number theorem for closed orbits of axiom {A} flows }, Journal = { Ann.\ of Math. }, Volume = { 118 }, Pages = { 573-591 }, Year = { 1983 } } @Article{ Pat81, Author = { E.M. Patterson }, Title = { {A} class of critical {R}iemanniann metrics }, Journal = { J. London Math.\ Soc. }, Volume = { 12 }, Pages = { 349-358 }, Year = { 1981 } } @Article{ Pau88, Author = { G. Paulik }, Title = { {O}n the continuity of harmonic mappings and the boundary }, Journal = { Manuscripta Math. }, Volume = { 62 }, Pages = { 127-130 }, Year = { 1988 } } @Misc{ Ped, Author = { F. Pedit }, Title = { {T}he tension field of the conformal {G}auss map } } @Article{ PedWu95, Author = { F. Pedit and H. Wu }, Title = { {D}iscretizing constant curvature surfaces via loop group factorizations: the discrete sine- and sinh-{G}ordon equations }, Journal = { J. Geom.\ Phys. }, Volume = { 17 }, Pages = { 245-260 }, Year = { 1995 } } @Unpublished{ Pen, Author = { C.K. Peng }, Title = { {S}ome new examples of minimal surfaces in {${\bf {R}}^3$} and its applications }, Note = { preprint } } @Incollection{ Pen84, Author = { C.K. Peng }, Title = { {A} remark on minimal surfaces in {${\bf {R}}^4$} }, Booktitle = { {P}roc. {S}econd {C}onference {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei 1981 }, Publisher = { Sci.\ Press }, Address = { Beijing }, Pages = { 307-308 }, Year = { 1984 } } @Article{ Pen84A, Author = { C.K. Peng }, Title = { {S}ome relations between minimal submanifolds and harmonic maps }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 5 }, Pages = { 85-89 }, Note = { (Chinese. English summary: {\it ibid} A{\bf 5} (1984),85-90) }, Year = { 1984 } } @Unpublished{ PenTan95, Author = { C.K. Peng and Z.Z. Tang }, Title = { {B}rouwer degrees of isoparametric maps between spheres }, Note = { Preprint }, Year = { 1995 } } @Unpublished{ PenTan95A, Author = { C.K. Peng and Z.Z. Tang }, Title = { {O}n representing homotopy classes of spheres by harmonic maps }, Note = { Preprint }, Year = { 1995 } } @Incollection{ PenTer83, Author = { C.K. Peng and C.L. Terng }, Title = { {M}inimal hypersurfaces of spheres with constant scalar curvature }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 177-198 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Article{ Per81, Author = { R. Percacci }, Title = { {G}lobal definition of nonlinear {$\sigma$}-models and some consequences }, Journal = { J. Math.\ Phys. }, Volume = { 22 }, Pages = { 1892-1895 }, Year = { 1981 } } @Incollection{ PerVer88, Author = { A. Pereira~do~Valle and A. Verjovsky }, Title = { {T}wo examples of escaping harmonic maps }, Booktitle = { {P}roc. {V}{I} {C}oll. {D}iff. {G}eo. {S}antiago }, Publisher = { Univ.\ de Santiago }, Address = { Santiago de Compostela }, Volume = { 61 }, Pages = { 219-229 }, Series = { Cursos e Congresos de Univ.\ de Santiago }, Year = { 1988 } } @Article{ Per81A, Author = { A.M. Perelomov }, Title = { {S}olutions of the instanton type in chiral models }, Journal = { Uspekhi Fiz.\ Nauk }, Volume = { 134 }, Pages = { 577-609 }, Year = { 1981 } } @Article{ Per87, Author = { A.M. Perelomov }, Title = { {C}hiral models: geometrical aspects }, Journal = { Phys.\ Rep. }, Volume = { 146 }, Pages = { 135-213 }, Year = { 1987 } } @Article{ Per89, Author = { A.M. Perelomov }, Title = { {S}upersymmetric chiral models: geometric aspects }, Journal = { Phys.\ Rep. }, Volume = { 174 }, Pages = { 229-282 }, Year = { 1989 } } @Article{ PerRos93, Author = { J. Perez and A. Ros }, Title = { {S}ome uniqueness and non-existence theorems for embedded minimal submanifolds }, Journal = { Math.\ Ann. }, Volume = { 295 }, Pages = { 513-525 }, Year = { 1993 } } @Article{ Pet94, Author = { R. Petit }, Title = { {O}n the rigidity of minimal immersions and pluriharmonic immersions }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 318 }, Pages = { 1125-1128 }, Year = { 1994 } } @Article{ Pet76, Author = { N.C. Petridis }, Title = { {P}icard's theorem for a family of non-holomorphic mappings of complex manifolds }, Journal = { Tensor (N.S.) }, Volume = { 30 }, Pages = { 179-185 }, Year = { 1976 } } @Article{ Pet77, Author = { N.C. Petridis }, Title = { {U}n th\'eor\`eme g\'en\'eral du type {P}icard }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 285 }, Pages = { 265-267 }, Year = { 1977 } } @Article{ PetRat90, Author = { V. Pettinati and A. Ratto }, Title = { {E}xistence and non-existence results for harmonic maps between spheres }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 17 }, Pages = { 273-282 }, Year = { 1990 } } @Article{ Pie88, Author = { B. Piette }, Title = { {E}xplicit solutions of {G}rassmannian {$\sigma$}-models }, Journal = { J. Math.\ Phys. }, Volume = { 29 }, Pages = { 2190-2196 }, Year = { 1988 } } @Incollection{ Pie88A, Author = { B. Piette }, Title = { {S}ome solutions of the {${U}({N})$} sigma modles }, Booktitle = { {G}roup theoretical methods in physics ({V}arna 1987) }, Publisher = { Springer }, Address = { Berlin }, Volume = { 313 }, Series = { Lecture Notes in Phys. }, Year = { 1988 } } @Misc{ PieStoZak, Author = { B. Piette and I. Stokoe and W.J. Zakrzewski }, Title = { {O}n stability of solutions of the {${U}({N})$} chiral model in two dimensions } } @Article{ PieZak88, Author = { B. Piette and W.J. Zakrzewski }, Title = { {G}eneral solutions of the {${U}(3)$} and {${U}(4)$} chiral models in two dimensions }, Journal = { Nuclear Phys.\ B }, Volume = { 300 }, Pages = { 207-222 }, Year = { 1988 } } @Article{ PieZak88A, Author = { B. Piette and W.J. Zakrzewski }, Title = { {P}roperties of classical solutions of the {${U}(n)$} chiral {$\sigma$}-models in two dimensions }, Journal = { Nuclear Phys.\ B }, Volume = { 300 }, Pages = { 223-237 }, Year = { 1988 } } @Article{ PieZak89, Author = { B. Piette and W.J. Zakrzewski }, Title = { {G}eneral solutions of the {${U}({N})$} chiral {$\sigma$}-models in two dimensions }, Journal = { J. Math.\ Phys. }, Volume = { 30 }, Pages = { 2233-2237 }, Year = { 1989 } } @Article{ Pin85, Author = { U. Pinkall }, Title = { {H}opf tori in {${S}^3$} }, Journal = { Invent.\ Math. }, Volume = { 81 }, Pages = { 379-386 }, Year = { 1985 } } @Article{ Pin86, Author = { U. Pinkall }, Title = { {I}nequalities of {W}illmore type for submanifolds }, Journal = { Math.\ Z. }, Volume = { 193 }, Pages = { 241-246 }, Year = { 1986 } } @Article{ PinPol93, Author = { U. Pinkall and K. Polthier }, Title = { {C}omputing discrete minimal surfaces and their conjugates }, Journal = { Experiment.\ Math. }, Volume = { 2 }, Pages = { 15-36 }, Year = { 1993 } } @Unpublished{ PinSte86, Author = { U. Pinkall and I. Sterling }, Title = { {W}illmore surfaces }, Note = { Preprint, MPI Bonn }, Year = { 1986 } } @Article{ PinSte89, Author = { U. Pinkall and I. Sterling }, Title = { {O}n the classification of constant mean curvature tori }, Journal = { Ann.\ of Math. }, Volume = { 130 }, Pages = { 407-451 }, Year = { 1989 } } @Article{ Pir, Author = { G.P. Pirola }, Title = { {T}he infinitesimal variation of spin abelian differentials and minimal surfaces }, Journal = { Comm.\ Anal.\ Geom. } } @Book{ Pit, Author = { J.T. Pitts }, Title = { {C}onstruction of minimal surfaces by variational methods in the large and applications }, Publisher = { Universit{\"a}t Bonn }, Address = { Bonn }, Volume = { 5 }, Series = { Vorlesungsreihe SFB 256 } } @Unpublished{ PitA, Author = { J.T. Pitts }, Title = { {T}he index of instability of minimal surfaces obtained by variational methods in the large }, Note = { preprint } } @Misc{ PitB, Author = { J.T. Pitts }, Title = { {A} three-sphere with an arbitrary metric supports at least four embedded minimal two-spheres } } @Article{ Pit76, Author = { J.T. Pitts }, Title = { {E}xistence and regularity of minimal surfaces on {R}iemannian manifolds }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 82 }, Pages = { 503-504 }, Year = { 1976 } } @Book{ Pit81, Author = { J.T. Pitts }, Title = { {E}xistence and regularity of minimal surfaces on {R}iemannian manifolds }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 27 }, Series = { Math.\ Notes }, Year = { 1981 } } @Article{ PitRub, Author = { J.T. Pitts and J.H. Rubinstein }, Title = { {A}pplications of minimax to minimal surfaces and the topology of {$3$}-manifolds }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Note = { (to appear) } } @Article{ PitRub86, Author = { J.T. Pitts and J.H. Rubinstein }, Title = { {E}xistence of minimal surfaces of bounded topological type in three-manifolds }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 10 }, Pages = { 163-176 }, Year = { 1986 } } @Article{ PitRub88, Author = { J.T. Pitts and J.H. Rubinstein }, Title = { {E}quivariant minimax and minimal surfaces in geometric three manifolds }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 19 }, Pages = { 303-309 }, Year = { 1988 } } @Article{ Piu82, Author = { M.P. Piu }, Title = { {C}ampi di vettori e applicazioni armoniche }, Journal = { Rend.\ Sem.\ Fac.\ Sci.\ Univ.\ Cagliari }, Volume = { 52 }, Pages = { 85-94 }, Year = { 1982 } } @Article{ Plu80, Author = { A.I. Pluzhnikov }, Title = { {H}armonic mappings of {R}iemannian surfaces and foliated manifolds }, Journal = { Mat.\ Sb. }, Volume = { 113 }, Pages = { 339-347 }, Year = { 1980 } } @Article{ Plu83, Author = { A.I. Pluzhnikov }, Title = { {S}ome properties of harmonic mappings in the case of spheres and {L}ie groups }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 268 }, Pages = { 1300-1302 }, Year = { 1983 } } @Incollection{ Plu84, Author = { A.I. Pluzhnikov }, Title = { {T}he indices of harmonic maps of spheres }, Booktitle = { {G}eometria i {T}opologia v {G}lobal'nyi {N}elineinykh {Z}adachakh ({G}eometry and {T}opology in {G}lobal {N}onlinear {P}roblems) }, Publisher = { Voronezh State University }, Address = { Voronezh }, Pages = { 162-166 }, Series = { Novoe Global Anal. }, Year = { 1984 } } @Book{ Plu84A, Author = { A.I. Pluzhnikov }, Title = { {Z}adacha {M}inimizatsii {F}unkstionala {E}nergii ({T}he problem of minimizing the energy functional) }, Publisher = { VINITI }, Address = { Moscow }, Note = { (Russian) }, Year = { 1984 } } @Article{ Plu85, Author = { A.I. Pluzhnikov }, Title = { {S}ome geometric properties of harmonic mappings }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 22 }, Pages = { 132-147 }, Note = { (Russian) }, Year = { 1985 } } @Article{ Plu86, Author = { A.I. Pluzhnikov }, Title = { {O}n the minima of the {D}irichlet functional }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 290 }, Number = { 2 }, Pages = { 289-293 }, Year = { 1986 } } @Incollection{ Plu86A, Author = { A.I. Pluzhnikov }, Title = { {A} topological criterion for the attainability of global minima of an energy functional }, Booktitle = { {A}nalysis on manifolds and differential equations }, Publisher = { Voronezh.\ Gos.\ Univ. }, Address = { Voronezh }, Pages = { 149-155 }, Note = { (Russian) }, Series = { Novoe Global Anal. }, Year = { 1986 } } @Incollection{ Plu93, Author = { A.I. Pluzhnikov }, Title = { {T}opological aspects of the problem of minimizing the {D}irichlet functional }, Booktitle = { {T}opology and its {A}pplications }, Editor = { S.P. Novikov }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 193 }, Pages = { 167-171 }, Series = { Proc.\ Steklov Inst.\ Math. }, Year = { 1993 } } @Book{ Pog75, Author = { A.V. Pogorelov }, Title = { {T}he {M}inkowski multidimensional problem }, Publisher = { Nauka }, Year = { 1975 } } @Article{ Pog81, Author = { A.V. Pogorelov }, Title = { {O}n the stability of minimal surfaces }, Journal = { Soviet Math.\ Dokl. }, Volume = { 24 }, Pages = { 274-276 }, Year = { 1981 } } @Article{ Poh76, Author = { K. Pohlmeyer }, Title = { {I}ntegrable {H}amiltonian systems and interaction through quadratic constants }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 46 }, Pages = { 207-221 }, Year = { 1976 } } @Incollection{ Pol84, Author = { J.C. Polking }, Title = { {A} survey of removable singularities }, Booktitle = { {S}eminar on nonlinear partial differential equations }, Editor = { S.S. Chern }, Publisher = { Springer }, Address = { Berlin }, Volume = { 2 }, Pages = { 261-292 }, Series = { MSRI Publ. }, Year = { 1984 } } @Misc{ Pol, Author = { K. Polthier }, Title = { {N}eue {M}inimalfl{\"a}chen in {${H}^3$} } } @Incollection{ Pol91, Author = { K. Polthier }, Title = { {G}eometric data for triply periodic minimal surfaces in spaces of constant curvature }, Booktitle = { {G}eometric {A}nalysis and {C}omputer {G}raphics }, Editor = { P. Concus and R. Finn and D.A. Hoffman }, Publisher = { Springer }, Address = { Berlin }, Volume = { 17 }, Series = { MSRI Publ. }, Year = { 1991 } } @Article{ Pon92, Author = { M. Pontecorvo }, Title = { {O}n twistor spaces of anti-self-dual {H}ermitian surfaces }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 331 }, Pages = { 653-661 }, Year = { 1992 } } @Article{ Poo91, Author = { C.C. Poon }, Title = { {S}ome new harmonic maps from {${B}^3$} to {${S}^n$} }, Journal = { J. Differential Geom. }, Volume = { 34 }, Pages = { 165-168 }, Year = { 1991 } } @Unpublished{ Poo83, Author = { Y.S. Poon }, Title = { {M}inimal surfaces in four dimensional manifolds }, Note = { M.Sc. thesis, Oxford, }, Year = { 1983 } } @Unpublished{ Poo84, Author = { Y.S. Poon }, Title = { {A}n integral representation of the twistor degree }, Note = { Oxford preprint }, Year = { 1984 } } @Article{ Poo88, Author = { Y.S. Poon }, Title = { {A}lgebraic dimension of twistor spaces }, Journal = { Math.\ Ann. }, Volume = { 282 }, Pages = { 621-627 }, Year = { 1988 } } @Article{ Poo92, Author = { Y.S. Poon }, Title = { {A}lgebraic structure of twistor spaces }, Journal = { J. Differential Geom. }, Volume = { 36 }, Pages = { 451-492 }, Year = { 1992 } } @Article{ Pre80, Author = { A.N. Pressley }, Title = { {D}ecomposition of the space of loops on a {L}ie group }, Journal = { Topology }, Volume = { 19 }, Pages = { 65-79 }, Year = { 1980 } } @Article{ Pre82, Author = { A.N. Pressley }, Title = { {T}he energy flow on the loop space of a compact {L}ie group }, Journal = { J. London Math.\ Soc. }, Volume = { 26 }, Pages = { 557-566 }, Year = { 1982 } } @Book{ PreSeg, Author = { A.N. Pressley and G. Segal }, Title = { {L}oop groups }, Publisher = { Clarendon Press }, Address = { Oxford }, Volume = { 1986 }, Series = { Oxford Math.\ Monographs } } @Article{ Pri83, Author = { P. Price }, Title = { {A} monotonicity formula for {Y}ang--{M}ills fields }, Journal = { Manuscripta Math. }, Volume = { 43 }, Pages = { 131-166 }, Year = { 1983 } } @Book{ ProWei67, Author = { M.H. Protter and H.F. Weinberger }, Title = { {M}aximum principles in differential equations }, Publisher = { Prentice-Hall }, Year = { 1967 } } @Misc{ Qin, Author = { J. Qing }, Title = { {O}n singularities of the heat flow for harmonic maps from surfaces into spheres } } @Article{ Qin92, Author = { J. Qing }, Title = { {M}ultiple solutions of the {D}irichlet problem for harmonic maps from discs into {$2$}sphere }, Journal = { Manuscripta Math. }, Volume = { 77 }, Pages = { 435-446 }, Year = { 1992 } } @Article{ Qin92A, Author = { J. Qing }, Title = { {R}emarks on the {D}irichlet problem for harmonic maps from the disc into the {$2$}-sphere }, Journal = { Proc.\ Roy.\ Soc.\ Edinburgh Sect.\ A }, Volume = { 122 }, Pages = { 63-67 }, Year = { 1992 } } @Article{ Qin93, Author = { J. Qing }, Title = { {B}oundary regularity of weakly harmonic maps from surfaces }, Journal = { J. Funct.\ Anal. }, Volume = { 114 }, Pages = { 458-466 }, Year = { 1993 } } @Article{ Qin93A, Author = { J. Qing }, Title = { {T}he {D}irichlet problem for harmonic maps from the disc into {K}{\"a}hler manifolds }, Journal = { J. London Math.\ Soc. }, Volume = { 47 }, Pages = { 182-192 }, Year = { 1993 } } @Article{ Rab93, Author = { M. Rabelo }, Title = { {H}armonic maps into surfaces with two-dimensional cone metrics }, Journal = { Mat.\ Contemp. }, Volume = { 4 }, Pages = { 139-151 }, Year = { 1993 } } @Article{ Rad30, Author = { T. Rado }, Title = { {O}n the problem of least area and the problem of {P}lateau }, Journal = { Math.\ Z. }, Volume = { 32 }, Pages = { 763-796 }, Year = { 1930 } } @Article{ Rai81, Author = { L.M. Raileanu }, Title = { {C}ritical sections of a {R}iemannian fibre bundle }, Journal = { Ann.\ Univ.\ Al.\ I. Cuza Iasi }, Volume = { 27 }, Pages = { 157-162 }, Year = { 1981 } } @Unpublished{ RalTot, Author = { S. Rallis and G. Toth }, Title = { {H}armonic maps with symmetries }, Note = { preprint } } @Unpublished{ Ram, Author = { J. Ramanathan }, Title = { {M}inimal and constant mean curvature surfaces in various {R}iemannian and {L}orentzian symmetric spaces }, Note = { preprint } } @Article{ Ram84, Author = { J. Ramanathan }, Title = { {H}armonic maps from {${S}^2$} to {${G}_{2,4}$} }, Journal = { J. Differential Geom. }, Volume = { 19 }, Pages = { 207-219 }, Year = { 1984 } } @Incollection{ Ram85, Author = { J. Ramanathan }, Title = { {H}armonic maps from surfaces to the complex {G}rassman manifolds }, Booktitle = { {T}opics in several complex variables }, Editor = { E. Ram{\'\i}rez~de~Arellano and D. Sundararaman }, Publisher = { Pitman }, Address = { London }, Volume = { 112 }, Pages = { 148-151 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Article{ Ram86, Author = { J. Ramanathan }, Title = { {A} remark on the energy of harmonic maps between spheres }, Journal = { Rocky Mountain J. Math. }, Volume = { 16 }, Pages = { 783-790 }, Year = { 1986 } } @Article{ Ram86A, Author = { J. Ramanathan }, Title = { {A} remark on the energy of harmonic maps between spheres }, Journal = { Rocky Mountain J. Math. }, Volume = { 16 }, Pages = { 783-790 }, Year = { 1986 } } @Article{ Ram90, Author = { J. Ramanathan }, Title = { {M}inimal hypersurfaces in {${S}^4$} with vanishing {G}auss--{K}ronecker curvature }, Journal = { Math.\ Z. }, Volume = { 205 }, Pages = { 645-658 }, Year = { 1990 } } @Article{ Ran91, Author = { Z. Ran }, Title = { {S}tability of certain holomorphic maps }, Journal = { J. Differential Geom. }, Volume = { 34 }, Pages = { 37-47 }, Year = { 1991 } } @Article{ Ran85, Author = { A. Ranjan }, Title = { {R}iemannian submersions of spheres with totally geodesic fibres }, Journal = { Osaka J. Math. }, Volume = { 22 }, Pages = { 243-260 }, Year = { 1985 } } @Article{ Ran86, Author = { A. Ranjan }, Title = { {O}n a remark of {O}'{N}eill }, Journal = { Duke Math.\ J. }, Volume = { 53 }, Pages = { 113-115 }, Year = { 1986 } } @Article{ Ran86A, Author = { A. Ranjan }, Title = { {R}iemannian submersions of compact simple {L}ie groups with connected totally geodesic fibres }, Journal = { Math.\ Z. }, Volume = { 191 }, Pages = { 239-246 }, Year = { 1986 } } @Article{ Ras78, Author = { T.M. Rassias }, Title = { {M}orse theory and {P}lateau's problem }, Journal = { Eleutheria }, Pages = { 209-249 }, Year = { 1978 } } @Article{ Ras79, Author = { T.M. Rassias }, Title = { {G}lobal analysis of the {M}orse-{S}male index for a minimal immersion in {${\bf {R}}^n$}, {$n\ge 3$} and its application to the classification problem of unstable minimal immersions }, Journal = { Eleutheria }, Pages = { 233-300 }, Year = { 1979 } } @Incollection{ Ras84, Author = { T.M. Rassias }, Title = { {O}n some problems of harmonic mappings and the {P}oincar{\'e} inequality }, Booktitle = { {C}omplex analysis and applications '81 ({V}arna 1981) }, Publisher = { Bulgarian Acad.\ Sci. }, Address = { Sofia }, Pages = { 453-457 }, Year = { 1984 } } @Book{ Ras86, Author = { T.M. Rassias }, Title = { {F}oundation of global nonlinear analysis }, Publisher = { Teubner }, Address = { Leipzig }, Volume = { 86 }, Series = { Teubner Texte Math. }, Year = { 1986 } } @Article{ Ras86A, Author = { T.M. Rassias }, Title = { {O}n the {M}orse-{S}male index theorem and the problem of minimal surfaces }, Journal = { Serdica }, Volume = { 12 }, Pages = { 238-244 }, Year = { 1986 } } @Incollection{ Ras87, Author = { T.M. Rassias }, Title = { {S}urvey on uniqueness and classification theorems for minimal surfaces }, Booktitle = { {N}onlinear analysis }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 493-511 }, Year = { 1987 } } @Article{ Rat87, Author = { A. Ratto }, Title = { {C}onstruction d'applications harmoniques de sph\`eres euclidiennes }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 304 }, Pages = { 185-186 }, Year = { 1987 } } @Unpublished{ Rat87A, Author = { A. Ratto }, Title = { {H}armonic maps of spheres and equivariant theory }, Note = { Thesis U. Warwick }, Year = { 1987 } } @Article{ Rat88, Author = { A. Ratto }, Title = { {O}n harmonic maps between {${S}^3$} and {${S}^2$} of prescribed {H}opf invariant }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 104 }, Pages = { 273-276 }, Year = { 1988 } } @Article{ Rat89, Author = { A. Ratto }, Title = { {E}quivariant harmonic maps between manifolds with metrics of {$(p,q)$}-signature }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 6 }, Pages = { 503-524 }, Year = { 1989 } } @Article{ Rat89A, Author = { A. Ratto }, Title = { {H}armonic maps from deformed spheres to spheres }, Journal = { Amer.\ J. Math. }, Volume = { 111 }, Pages = { 225-238 }, Year = { 1989 } } @Article{ Rat89B, Author = { A. Ratto }, Title = { {H}armonic maps of spheres and the {H}opf construction }, Journal = { Topology }, Volume = { 28 }, Pages = { 379-388 }, Year = { 1989 } } @Article{ Rat89C, Author = { A. Ratto }, Title = { {O}n the {D}irichlet problem for harmonic maps into spheres or ellipsoids and equivariant harmonic maps from warped products }, Journal = { Bull.\ Soc.\ Math.\ Belg. }, Volume = { 41 }, Pages = { 145-168 }, Year = { 1989 } } @Article{ RatRig93, Author = { A. Ratto and M. Rigoli }, Title = { {E}lliptic differential inequalities with applications to harmonic maps }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 45 }, Pages = { 321-337 }, Year = { 1993 } } @Article{ RatRig93A, Author = { A. Ratto and M. Rigoli }, Title = { {O}n the asymptotic behaviour of rotationally symmetric harmonic maps }, Journal = { J. Differential Equations }, Volume = { 101 }, Pages = { 15-27 }, Year = { 1993 } } @Unpublished{ RatRigVer, Author = { A. Ratto and M. Rigoli and L. V{\'e}ron }, Title = { {E}quations aux d\'eriv\'ees partielles }, Note = { preprint } } @Article{ RatRigVer92, Author = { A. Ratto and M. Rigoli and L. V{\'e}ron }, Title = { {C}ourbure scalaire et d{\'e}formations conformes de l'espace hyperbolique }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 315 }, Pages = { 1153-1158 }, Year = { 1992 } } @Article{ RatRigVer94, Author = { A. Ratto and M. Rigoli and L. V{\'e}ron }, Title = { {C}onformal immersions of {R}iemannian manifolds and extensions of the {S}chwarz {L}emma }, Journal = { Duke Math.\ J. }, Pages = { 223-236 }, Year = { 1994 } } @Article{ RatRigVer94A, Author = { A. Ratto and M. Rigoli and L. V{\'e}ron }, Title = { {C}ourbure scalaire et d{\'e}formations conformes des vari{\'e}t{\'e}s riemanniennes non compactes }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 318 }, Pages = { 665-670 }, Year = { 1994 } } @Article{ RatRigVer94B, Author = { A. Ratto and M. Rigoli and L. V{\'e}ron }, Title = { {S}calar curvature and conformal deformation of hyperbolic space }, Journal = { J. Funct.\ Anal. }, Volume = { 121 }, Pages = { 15-77 }, Year = { 1994 } } @Article{ Rau65, Author = { H.E. Rauch }, Title = { {A} transcendental view of the space of algebraic {R}iemann surfaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 71 }, Pages = { 1-39 }, Year = { 1965 } } @Unpublished{ Raw, Author = { J. Rawnsley }, Title = { {G}eneralized twistor spaces and isotropic maps of {R}iemann surfaces }, Note = { preprint } } @Unpublished{ RawA, Author = { J. Rawnsley }, Title = { {T}he twistor relationship between the {V}eronese maps {${S}^2\to {S}^4$} and {${\bf {C}}{P}^n\to {\bf {C}}{P}^3$} }, Note = { Warwick preprint } } @Unpublished{ RawB, Author = { J. Rawnsley }, Title = { {T}wistor spaces and isotropic harmonic maps of {R}iemann surfaces }, Note = { preprint } } @Article{ Raw83, Author = { J. Rawnsley }, Title = { {O}n the rank of horizontal maps }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 92 }, Pages = { 485-488 }, Year = { 1983 } } @Unpublished{ Raw84, Author = { J. Rawnsley }, Title = { {E}quivariant harmonic maps }, Note = { Warwick preprint }, Year = { 1984 } } @Incollection{ Raw84A, Author = { J. Rawnsley }, Title = { {N}oether's theorem for harmonic maps }, Booktitle = { {D}ifferential geometric methods in mathematical physics }, Editor = { S. Sternberg }, Publisher = { Reidel }, Address = { Dortrecht, Boston, London }, Volume = { 6 }, Pages = { 197-202 }, Series = { Math.\ Phys.\ Stud. }, Year = { 1984 } } @Incollection{ Raw85, Author = { J. Rawnsley }, Title = { {$f$}-structures, {$f$}-twistor spaces and harmonic maps }, Booktitle = { {G}eometry {S}eminar ``{L}uigi {B}ianchi'' {I}{I}---1984 }, Editor = { E. Vesentini }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1164 }, Pages = { 85-159 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Incollection{ Raw88, Author = { J. Rawnsley }, Title = { {H}armonic {$2$}-spheres }, Booktitle = { {Q}uantum {T}heories and {G}eometry }, Editor = { M. Cahen and M. Flato }, Publisher = { Kluwer Acad.\ Publ. }, Address = { Dordrecht }, Pages = { 175-189 }, Year = { 1988 } } @Incollection{ Raw88A, Author = { J. Rawnsley }, Title = { {S}tability of harmonic maps into symmetric spaces }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 203-209 }, Year = { 1988 } } @Incollection{ Raw92, Author = { J.H. Rawnsley }, Title = { {T}wistor theory for {R}iemannian manifolds }, Booktitle = { {N}ew {D}evelopments in {L}ie {T}heory and {T}heir {A}pplications }, Editor = { J. Tirao and N. Wallach }, Publisher = { Birkh\"auser }, Address = { Boston, Basel, Stuttgart }, Volume = { 105 }, Pages = { 115--128 }, Series = { Progr.\ Math. }, Year = { 1992 } } @Article{ Rei76, Author = { E. Reich }, Title = { {A} generalized {D}irichlet integral }, Journal = { J. Analyse Math. }, Volume = { 30 }, Pages = { 456-463 }, Year = { 1976 } } @Article{ Rei85, Author = { E. Reich }, Title = { {O}n the variational principle of {G}erstenhaber and {R}auch }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { 10 }, Pages = { 469-475 }, Year = { 1985 } } @Article{ Rei86, Author = { E. Reich }, Title = { {H}armonic mappings and quasiconformal mappings. }, Journal = { J. Analyse Math. }, Volume = { 46 }, Pages = { 239-245. }, Year = { 1986 } } @Article{ Rei87, Author = { E. Reich }, Title = { {T}he composition of harmonic mappings }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { 12 }, Pages = { 47-53 }, Year = { 1987 } } @Article{ Rei87A, Author = { E. Reich }, Title = { {L}ocal decomposition of harmonic mappings }, Journal = { Complex Variables Theory Appl. }, Volume = { 9 }, Pages = { 263-269 }, Year = { 1987 } } @Incollection{ Rei71, Author = { R.C. Reilly }, Title = { {V}ariational properties of mean curvatures }, Booktitle = { {P}roc. {S}em. 13th {B}iennial {C}and. {M}ath. {C}ongress {I}{I} }, Pages = { 102-114 }, Year = { 1971 } } @Article{ Rei73, Author = { R.C. Reilly }, Title = { {V}ariational properties of functions of the mean curvatures for hypersurfaces in space forms }, Journal = { J. Differential Geom. }, Volume = { 8 }, Pages = { 465-477 }, Year = { 1973 } } @Article{ Rei77, Author = { R.C. Reilly }, Title = { {A}pplications of the {H}essian operator in a {R}iemannian manifold }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 26 }, Pages = { 459-472 }, Year = { 1977 } } @Article{ Rei82, Author = { R.C. Reilly }, Title = { {M}ean curvature, the {L}aplacian and soap bubbles }, Journal = { Amer.\ Math.\ Monthly }, Volume = { 89 }, Pages = { 180-188, 197-198 }, Year = { 1982 } } @Incollection{ Rei82A, Author = { C. Reina }, Title = { {A}lgebraic geometrical methods in field theory; the example of {${C}{P}^n$} models }, Booktitle = { {P}roc. {G}eo. {P}hysics }, Pages = { 263-270 }, Year = { 1982 } } @Incollection{ Rei83, Author = { C. Reina }, Title = { {O}n the harmony of the {E}rnst equation }, Booktitle = { {P}roc. {T}hird {M}. {G}rossmann {M}eeting on {G}en. {R}el. }, Publisher = { North Holland }, Pages = { 1029-1032 }, Year = { 1983 } } @Article{ RemSte60, Author = { R. Remmert and K. Stein }, Title = { {E}igentliche holomorphe {A}bbildungen }, Journal = { Math.\ Z. }, Volume = { 73 }, Pages = { 159-189 }, Year = { 1960 } } @Article{ Remvan61, Author = { R. Remmert and T. van~de~Ven }, Title = { \"{U}ber holomorphe {A}bbildungen projektivalgebraischer {M}annigfaltigkeiten auf komplexe {R}\"aume }, Journal = { Math.\ Ann. }, Volume = { 142 }, Pages = { 453-486 }, Year = { 1961 } } @Article{ Res68, Author = { Y.G. Reshetnyak }, Title = { {N}onexpanding maps into a space of curvature no greater than {${K}$} }, Journal = { Siberian Math.\ J. }, Volume = { 6 }, Pages = { 918-927 }, Year = { 1968 } } @Book{ Res89, Author = { Y.G. Reshetnyak }, Title = { {S}pace mappings with bounded dilatation }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 73 }, Series = { Transl.\ Math.\ Monographs }, Year = { 1989 } } @Article{ Rey91, Author = { O. Rey }, Title = { {H}eat flow for the equation of surfaces with prescribed mean curvature }, Journal = { Math.\ Ann. }, Volume = { 291 }, Pages = { 123-146 }, Year = { 1991 } } @Article{ Rez92, Author = { A.G. Reznikov }, Title = { {L}inearization and explicit solutions of the minimal surface equation }, Journal = { Publ.\ Mat. }, Volume = { 36 }, Pages = { 39-46 }, Year = { 1992 } } @Article{ Rez93, Author = { A.G. Reznikov }, Title = { {H}armonic maps, hyperbolic cohomology and higher {M}ilnor inequalities }, Journal = { Topology }, Volume = { 32 }, Pages = { 899-907 }, Year = { 1993 } } @Article{ Rez93A, Author = { A.G. Reznikov }, Title = { {S}ymplectic twistor spaces }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 11 }, Pages = { 109-118 }, Year = { 1993 } } @Misc{ Rig, Author = { M. Rigoli }, Title = { {O}n a conformal {B}ernstein's type property } } @Misc{ RigA, Author = { M. Rigoli }, Title = { {O}n immersed compact submanifolds of {E}uclidean space } } @Article{ Rig85, Author = { M. Rigoli }, Title = { {A} rigidity result for holomorphic immersions of surfaces in {${C}{P}^n$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 93 }, Pages = { 317-320 }, Year = { 1985 } } @Article{ Rig86, Author = { M. Rigoli }, Title = { {T}he harmonicity of the spherical {G}auss map }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 18 }, Pages = { 609-612 }, Year = { 1986 } } @Article{ Rig87, Author = { M. Rigoli }, Title = { {T}he conformal {G}auss map of submanifolds of the {M}\"obius space }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 5 }, Pages = { 97-116 }, Year = { 1987 } } @Misc{ RigSal, Author = { M. Rigoli and I. Salavessa }, Title = { {G}eometrical properties via almost conformal vector fields } } @Article{ RigSal87, Author = { M. Rigoli and I. Salavessa }, Title = { {C}onformal and isometric immersions of {R}iemannian manifolds }, Journal = { Math.\ Z. }, Volume = { 196 }, Pages = { 293-300 }, Year = { 1987 } } @Article{ RigSal93, Author = { M. Rigoli and I. Salavessa }, Title = { {W}illmore submanifolds of the {M}\"obius space and a {B}ernstein-type theorem }, Journal = { Manuscripta Math. }, Volume = { 81 }, Pages = { 203-222 }, Year = { 1993 } } @Article{ RigTri92, Author = { M. Rigoli and R. Tribuzy }, Title = { {T}he {G}auss map for {K}\"ahlerian submanifolds of {${\bf {R}}^n$} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 332 }, Pages = { 515-528 }, Year = { 1992 } } @Article{ RipTom, Author = { J. Ripoli and F. Tomi }, Title = { {M}aximum principles for minimal surfaces in {${\bf {R}}^3$} having noncompact boundary and a uniqueness theorem for the helicoid }, Journal = { Manuscripta Math. }, Volume = { 87 }, Pages = { 417-434 } } @Article{ Rip89, Author = { J.P. Ripoll }, Title = { {H}elicoidal minimal surfaces in hyperbolic spaces }, Journal = { Nagoya Math.\ J. }, Volume = { 114 }, Pages = { 65-75 }, Year = { 1989 } } @Article{ Rip89A, Author = { J.P. Ripoll }, Title = { {U}niqueness of minimal rotational surfaces in {${S}^3$} }, Journal = { Amer.\ J. Math. }, Volume = { 111 }, Pages = { 537-547 }, Year = { 1989 } } @Misc{ Rit, Author = { M. Ritor{\'e} }, Title = { {A}pplications of compactness results for harmonic maps to stable constant mean curvature surfaces } } @Article{ RitRos92, Author = { M. Ritor{\'e} and A. Ros }, Title = { {S}table constant mean curvature tori and the isoperimetric problem in three space forms }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 67 }, Pages = { 293-305 }, Year = { 1992 } } @Misc{ Riv, Author = { T. Rivi{\`e}re }, Title = { {F}lot des applications harmoniques en dimension deux } } @Article{ Riv91, Author = { T. Rivi{\`e}re }, Title = { {A}pplications harmoniques de {${B}^3$} dans {${S}^2$} ayant une ligne de singularit{\'e}s }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 313 }, Pages = { 583-587 }, Year = { 1991 } } @Article{ Riv92, Author = { T. Rivi{\`e}re }, Title = { {A}pplications harmoniques de {${B}^3$} dans {${S}^2$} partout discontinues }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 314 }, Pages = { 719-723 }, Year = { 1992 } } @Article{ RivSha91, Author = { T. Rivi{\`e}re and I. Shafir }, Title = { {A}symptotic analysis of minimizing harmonic maps of regions bounded by two circles }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 313 }, Pages = { 503-508 }, Year = { 1991 } } @Article{ Rom87, Author = { A. Romero }, Title = { {A}n extension of {C}alabi's rigidity theorem to complex submanifolds of indefinite complex space forms }, Journal = { Manuscripta Math. }, Volume = { 59 }, Pages = { 261-276 }, Year = { 1987 } } @Incollection{ RosVerVer85, Author = { A. Ros and P. Verheyen and L. Verstraelen }, Title = { {P}ositively curved minimal submanifolds }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Editor = { D. Ferus and R.B. Gardner and S. Helgason and U. Simon }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1156 }, Pages = { 280-295 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Article{ RosTou86, Author = { H. Rosenberg and E. Toubiana }, Title = { {D}eformations of complete minimal surfaces }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 295 }, Pages = { 475-489 }, Year = { 1986 } } @Article{ RosTou86A, Author = { H. Rosenberg and E. Toubiana }, Title = { {S}ome remark on deformations of minimal surfaces }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 295 }, Pages = { 491-499 }, Year = { 1986 } } @Article{ RosTou87, Author = { H. Rosenberg and E. Toubiana }, Title = { {A} cylindrical type complete minimal surface in a slab of {${\bf {R}}^3$} }, Journal = { Bull.\ Soc.\ Math.\ III }, Pages = { 241-245 }, Year = { 1987 } } @Article{ RosTou88, Author = { H. Rosenberg and E. Toubiana }, Title = { {C}omplete minimal surfaces and minimal herissons }, Journal = { J. Differential Geom. }, Volume = { 28 }, Pages = { 115-132 }, Year = { 1988 } } @Misc{ Ros, Author = { W. Rossman }, Title = { {F}oliations by constant mean curvature surfaces of {${\bf {R}}^3$} and {${\bf {H}}^3$} with singularities } } @Incollection{ Ros93, Author = { W. Rossman }, Title = { {N}ew examples of minimal surfaces }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 369-377 }, Year = { 1993 } } @Unpublished{ RosUmeYam, Author = { W. Rossman and M. Umehara and K. Yamada }, Title = { {I}rreducible constant mean curvature {$1$} surfaces in hyperbolic space with positive genus }, Note = { preprint } } @Article{ Roy80, Author = { H.L. Royden }, Title = { {T}he {A}hlfors--{S}chwarz lemma in several complex variables }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 55 }, Pages = { 547-558 }, Year = { 1980 } } @Article{ Ru91, Author = { M. Ru }, Title = { {O}n the {G}auss map of minimal surfaces immersed in {${R}^n$} }, Journal = { J. Differential Geom. }, Volume = { 34 }, Pages = { 411-423 }, Year = { 1991 } } @Article{ Ru93, Author = { M. Ru }, Title = { {G}auss map of minimal surfaces with ramification }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 339 }, Pages = { 751-764 }, Year = { 1993 } } @Article{ Rub88, Author = { P.J. Ruback }, Title = { {S}igma model solitons and their moduli space metrics }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 116 }, Pages = { 645-658 }, Year = { 1988 } } @Article{ Rub85, Author = { J.H. Rubinstein }, Title = { {E}mbedded minimal surfaces in {$3$}-manifolds with positive scalar curvature }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 95 }, Pages = { 458-462 }, Year = { 1985 } } @Article{ Ruc79, Author = { H. Ruchert }, Title = { {E}in {E}indeutigkeitssatz f\"ur {F}l\"achen konstanter mittlerer }, Journal = { Kr\"ummung Arch.\ Math. }, Volume = { 33 }, Pages = { 91-104 }, Year = { 1979 } } @Article{ Ruh70, Author = { E.A. Ruh }, Title = { {A}symptotic behaviour of non-parametric minimal hypersurfaces }, Journal = { J. Differential Geom. }, Volume = { 4 }, Pages = { 509-513 }, Year = { 1970 } } @Article{ Ruh71, Author = { E.A. Ruh }, Title = { {M}inimal immersions of {$2$}-spheres in {${S}^4$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 28 }, Pages = { 219-222 }, Year = { 1971 } } @Article{ RuhVil70, Author = { E.A. Ruh and J. Vilms }, Title = { {T}he tension field of the {G}auss map }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 149 }, Pages = { 569-573 }, Year = { 1970 } } @Misc{ Ruk, Author = { P. Rukimbira }, Title = { {H}armonic maps in contact geometry } } @Incollection{ SIaAMP96, Author = { S.Ianus and A.M.Pastore }, Title = { {H}armonic maps on {S}asakian and cosymplectic manifolds }, Booktitle = { {P}roceedings of the 24-th {N}{C}{G}{T}, {J}uly 5-9,1994, {T}imisoara {U}niv.,{R}omania }, Pages = { 139-155 }, Year = { 1996 } } @Article{ SIaAMP97, Author = { S.Ianus and A.M.Pastore }, Title = { {O}n harmonic maps on metric {$f$}-manifolds }, Journal = { Tensor (N.S.) }, Volume = { 54 }, Year = { 1997 } } @Article{ SIaLOrVVu95, Author = { S.Ianus and L.Ornea and V.Vuletescu }, Title = { {H}olomorphic and harmonic maps of local conformal {K}aehlerian manifolds }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 9 }, Pages = { 569-579 }, Year = { 1995 } } @Incollection{ SIaMVi91, Author = { S.Ianus and M.Visinescu }, Title = { {S}pace-time compactification and {R}iemannian submersion }, Booktitle = { {T}he {M}athematical {H}eritage of {C}.{F}.{G}auss }, Editor = { T.Rassias, }, Publisher = { World Scientific Press }, Address = { Singapore }, Pages = { 358-371 }, Year = { 1991 } } @Article{ SacUhl77, Author = { J. Sacks and K. Uhlenbeck }, Title = { {T}he existence of minimal immersions of two-spheres }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 83 }, Pages = { 1033-1036 }, Year = { 1977 } } @Article{ SacUhl81, Author = { J. Sacks and K. Uhlenbeck }, Title = { {T}he existence of minimal immersions of {$2$}-spheres }, Journal = { Ann.\ of Math. }, Volume = { 113 }, Pages = { 1-24 }, Year = { 1981 } } @Article{ SacUhl82, Author = { J. Sacks and K. Uhlenbeck }, Title = { {M}inimal immersions of closed {R}iemann surfaces }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 271 }, Pages = { 639-652 }, Year = { 1982 } } @Incollection{ Sak93, Author = { H. Sakagawa }, Title = { {O}n the construction of twistor lifts of harmonic 2-spheres into {${G}r_t({\bf {C}}^n)$} }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 451-455 }, Year = { 1993 } } @Article{ Sak94, Author = { H. Sakagawa }, Title = { {O}n the extended solutions of isotropic harmonic {$2$}-spheres lifted into {G}rassmannians }, Journal = { Algebras Groups Geom. }, Volume = { 11 }, Pages = { 37-52 }, Year = { 1994 } } @Unpublished{ Sak94A, Author = { H. Sakagawa }, Title = { {T}he uniton numbers of the harmonic {$2$}-spheres in {${G}r_2({\bf {C}}^n)$} }, Note = { Preprint }, Year = { 1994 } } @Unpublished{ Sak, Author = { M. Sakaki }, Title = { {H}armonicity of spherical {G}auss map and pinching of {S}imons type }, Note = { preprint } } @Misc{ SakA, Author = { M. Sakaki }, Title = { {O}n minimal surfaces with constant {K}{\"a}hler angle } } @Article{ SakB, Author = { M. Sakaki }, Title = { {O}n minimal surfaces with constant {K}{\"a}hler angle in {${C}{P}^3$} and {${C}{P}^4$} }, Journal = { Tsukuba J. Math. } } @Misc{ SakC, Author = { M. Sakaki }, Title = { {R}igidity of superconformal minimal surfaces lying in odd-dimensional unit spheres } } @Article{ Sak86, Author = { M. Sakaki }, Title = { {O}n the stability of minimal surfaces in {${S}^3$} }, Journal = { Kodai Math.\ J. }, Volume = { 9 }, Pages = { 421-424 }, Year = { 1986 } } @Article{ Sak87, Author = { M. Sakaki }, Title = { {A} uniqueness theorem for minimal surfaces in {${S}^3$} }, Journal = { Kodai Math.\ J. }, Volume = { 10 }, Pages = { 39-41 }, Year = { 1987 } } @Article{ Sak89, Author = { M. Sakaki }, Title = { {E}stimates on the stability of minimal surfaces and harmonic maps }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 41 }, Pages = { 641-650 }, Year = { 1989 } } @Article{ Sak89A, Author = { M. Sakaki }, Title = { {R}emarks on the rigidity and stability of minimal submanifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 106 }, Pages = { 793-795 }, Year = { 1989 } } @Article{ Sak90, Author = { M. Sakaki }, Title = { {S}tability of surfaces with constant mean curvature in {$3$}-dimensional {R}iemannian manifolds }, Journal = { Osaka J. Math. }, Volume = { 27 }, Pages = { 893-898 }, Year = { 1990 } } @Article{ Sak90A, Author = { M. Sakaki }, Title = { {U}pper bounds for the index of minimal surfaces }, Journal = { T\^ohoku Math.\ J. }, Volume = { 42 }, Pages = { 339--349 }, Year = { 1990 } } @Article{ Sak92, Author = { M. Sakaki }, Title = { {E}xceptional minimal surfaces whose {G}auss images have constant curvature }, Journal = { Tokyo J. Math. }, Volume = { 15 }, Pages = { 381--388 }, Year = { 1992 } } @Article{ Sak92A, Author = { M. Sakaki }, Title = { {E}xceptional minimal surfaces with the {R}icci condition }, Journal = { Tsukuba J. Math. }, Volume = { 16 }, Pages = { 161--167 }, Year = { 1992 } } @Article{ Sak94B, Author = { M. Sakaki }, Title = { {M}inimal {$2$}-tori in {${S}^4$} whose {G}auss images have constant curvature }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 62 }, Pages = { 470-474 }, Year = { 1994 } } @Article{ Sak94C, Author = { M. Sakaki }, Title = { {M}inimal surfaces with the {R}icci condition in {$4$}-dimensional space forms }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 121 }, Pages = { 573--577 }, Year = { 1994 } } @Unpublished{ Sak95, Author = { M. Sakaki }, Title = { {O}n minimal surfaces in {${\bf {R}}^n$} whose {G}auss images have constant curvature }, Note = { Preprint }, Year = { 1995 } } @Article{ Sak85, Author = { K. Sakamoto }, Title = { {H}elical minimal immersions of compact {R}iemannian manifolds into a unit sphere }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 285 }, Pages = { 765-790 }, Year = { 1985 } } @Article{ Sak91, Author = { K. Sakamoto }, Title = { {S}tability of the equator map }, Journal = { J. Reine Angew.\ Math. }, Volume = { 414 }, Pages = { 23-43 }, Year = { 1991 } } @Incollection{ Sal85, Author = { S.M. Salamon }, Title = { {H}armonic and holomorphic maps }, Booktitle = { {G}eometry {S}eminar ``{L}uigi {B}ianchi'' {I}{I}---1984 }, Editor = { E. Vesentini }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1164 }, Pages = { 161-224 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Incollection{ Sal85A, Author = { S.M. Salamon }, Title = { {M}inimal surfaces and symmetric spaces }, Booktitle = { {D}ifferential {G}eometry }, Editor = { L.A. Cordero }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 131 }, Pages = { 103-114 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Incollection{ Sal88, Author = { S.M. Salamon }, Title = { {D}egrees of minimal surfaces in {$4$}-manifolds }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 210-223 }, Year = { 1988 } } @Unpublished{ Sal88A, Author = { I. Salavessa }, Title = { {G}raphs with parallel mean curvature and a variational problem in conformal geometry }, Note = { Thesis, Warwick }, Year = { 1988 } } @Article{ Sal89, Author = { I. Salavessa }, Title = { {G}raphs with parallel mean curvature }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 107 }, Pages = { 449-458 }, Year = { 1989 } } @Article{ Sam78, Author = { J.H. Sampson }, Title = { {S}ome properties and applications of harmonic mappings }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 11 }, Pages = { 211-228 }, Year = { 1978 } } @Article{ Sam79, Author = { J.H. Sampson }, Title = { {F}oliations from quadratic and {H}ermitian differential forms }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 70 }, Pages = { 91-99 }, Year = { 1979 } } @Article{ Sam82, Author = { J.H. Sampson }, Title = { {E}ine parabolische {G}leichung mit verg\"anglichen {L}\"osungen }, Journal = { Manuscripta Math. }, Volume = { 40 }, Pages = { 87-89 }, Year = { 1982 } } @Incollection{ Sam82A, Author = { J.H. Sampson }, Title = { {O}n a class of harmonic maps }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 138-139 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ Sam82B, Author = { J.H. Sampson }, Title = { {O}n harmonic mappings }, Journal = { Sympos.\ Math. }, Volume = { 26 }, Pages = { 197-210 }, Year = { 1982 } } @Incollection{ Sam85, Author = { J.H. Sampson }, Title = { {H}armonic maps in {K}\"ahler gemetry }, Booktitle = { {H}armonic {M}aps and {M}inimal {I}mmersions }, Editor = { E. Giusti }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1161 }, Pages = { 193-205 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Incollection{ Sam86, Author = { J.H. Sampson }, Title = { {A}pplications of harmonic maps to {K}\"ahler geometry }, Booktitle = { {C}omplex differential geometry and non-linear differential equations }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 49 }, Pages = { 125-134 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Article{ SanSha94, Author = { E. Sandier and I. Shafir }, Title = { {O}n the uniqueness of minimizing harmonic maps to a closed hemisphere }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 2 }, Pages = { 113-122 }, Year = { 1994 } } @Article{ San91, Author = { {\'E}. Sandier }, Title = { {S}ym{\'e}trie des applications harmoniques minimisantes d'une couronne vers la sph{\`e}re }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 313 }, Pages = { 435-440 }, Year = { 1991 } } @Article{ San93, Author = { {\'E}. Sandier }, Title = { {M}inimisation de l'{\'e}nergie des cristaux liquides dans un cylindre }, Journal = { C. R. Acad.\ Sci.\ Paris S\'er.\ I Math. }, Volume = { 317 }, Pages = { 473-478 }, Year = { 1993 } } @Article{ San93A, Author = { {\'E}. Sandier }, Title = { {T}he symmetry of minimizing harmonic maps from a two dimensional domain to the sphere }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 10 }, Pages = { 549-559 }, Year = { 1993 } } @Article{ SanSha93, Author = { {\'E}. Sandier and I. Shafrir }, Title = { {O}n the symmetry of minimizing harmonic maps in {${N}$} dimensions }, Journal = { Differential Integral Equations }, Volume = { 6 }, Pages = { 1531-1541 }, Year = { 1993 } } @Article{ San83, Author = { A. Sanini }, Title = { {A}pplicazioni armoniche tra i fibrati tangenti di varieta riemanniane }, Journal = { Boll.\ Un.\ Mat.\ Ital.\ A }, Volume = { 2 }, Pages = { 55-64 }, Year = { 1983 } } @Article{ San83A, Author = { A. Sanini }, Title = { {A}pplicazioni tra variet\`a riemanniane con energia critica rispetto a deformazioni di metriche }, Journal = { Rend.\ Mat. }, Volume = { 3 }, Pages = { 53-63 }, Year = { 1983 } } @Article{ San85, Author = { A. Sanini }, Title = { {A}pplicazioni armoniche tra fibrati tangenti unitari }, Journal = { Rend.\ Sem.\ Mat.\ Univ.\ Politec.\ Torino }, Volume = { 43 }, Pages = { 159-170 }, Year = { 1985 } } @Article{ San88, Author = { A. Sanini }, Title = { {T}otal tension of a map and pseudo-umbilical submanifolds }, Journal = { Rend.\ Mat.\ Appl. }, Volume = { 8 }, Pages = { 519-526 }, Year = { 1988 } } @Article{ San92, Author = { A. Sanini }, Title = { {C}onformal variational problems }, Journal = { Rend.\ Circ.\ Mat.\ Palermo }, Volume = { 41 }, Pages = { 165-184 }, Year = { 1992 } } @Article{ San94, Author = { W. Santos }, Title = { {S}ubmanifolds with parallel mean curvature vector in spheres }, Journal = { T\^ohoku Math.\ J. }, Volume = { 46 }, Pages = { 403-415 }, Year = { 1994 } } @Misc{ Sas, Author = { R. Sasaki }, Title = { {E}xplicit forms of {B}{\"a}cklund transformations for the {G}rassmannian and {${C}{P}^{{N}-1}$} sigma models } } @Article{ Sas83, Author = { R. Sasaki }, Title = { {G}eneral classical solutions of the complex {G}rassmannian and {${C}{P}^{{N}-1}$} sigma model }, Journal = { Phys.\ Lett.\ B }, Volume = { 130 }, Pages = { 69-72 }, Year = { 1983 } } @Article{ Sas84, Author = { R. Sasaki }, Title = { {L}ocal theory of solutions for the complex {G}rassmannian and {${C}{P}^{n-1}$} sigma models }, Journal = { Z. Phys. }, Volume = { C24 }, Pages = { 163-170 }, Year = { 1984 } } @Article{ Sat93, Author = { P. Sattayatham }, Title = { {O}n the functions that preserve harmonicity in the {E}uclidean space }, Journal = { Southeast Asian Bull.\ Math. }, Volume = { 17 }, Pages = { 45-50 }, Year = { 1993 } } @Article{ Sau90, Author = { F. Sauvigny }, Title = { {C}urvature estimates for immersions of minimal surface type via uniformization and theorems of {B}ernstein type }, Journal = { Manuscripta Math. }, Volume = { 67 }, Pages = { 69-97 }, Year = { 1990 } } @Article{ Sau90A, Author = { F. Sauvigny }, Title = { {O}n immersions of constant mean curvature: compactness results and finiteness theorems for {P}lateau's problem }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 110 }, Pages = { 125-140 }, Year = { 1990 } } @Article{ Sch91, Author = { R. Schimming }, Title = { {H}armonic differential operators }, Journal = { Forum Math. }, Volume = { 3 }, Pages = { 177-203 }, Year = { 1991 } } @Misc{ Sch, Author = { R. Schoen }, Title = { {C}ompactness, regularity, and almost holomorphicity results for stable minimal surfaces in arbitrary codimension } } @Unpublished{ Sch77, Author = { R. Schoen }, Title = { {E}xistence and regularity for some geometric variational problems }, Note = { Thesis, Stanford Univ. }, Year = { 1977 } } @Article{ Sch82, Author = { R. Schoen }, Title = { {A} lower bound for the first eigenvalue of a negatively curved manifold }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 233-238 }, Year = { 1982 } } @Article{ Sch82A, Author = { R. Schoen }, Title = { {A} remark on minimal hypercones }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 79 }, Pages = { 4523-4524 }, Year = { 1982 } } @Incollection{ Sch83, Author = { R. Schoen }, Title = { {E}stimates for stable minimal surfaces in three dimensional manifolds }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 111-126 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Incollection{ Sch83A, Author = { R. Schoen }, Title = { {M}inimal surfaces and positive mean curvature }, Booktitle = { {P}roc. {I}.{C}.{M}. {W}arsaw }, Pages = { 575-578 }, Year = { 1983 } } @Article{ Sch83B, Author = { R. Schoen }, Title = { {U}niqueness, symmetry and embeddedness of minimal surfaces }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 791-809 }, Year = { 1983 } } @Incollection{ Sch84, Author = { R. Schoen }, Title = { {A}nalytic aspects of the harmonic map problem }, Booktitle = { {S}eminar on nonlinear partial differential equations }, Editor = { S.S. Chern }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 2 }, Pages = { 321-358 }, Series = { MSRI Publ. }, Year = { 1984 } } @Article{ Sch91A, Author = { R. Schoen }, Title = { {A} report on some recent progress on nonlinear problems in geometry }, Journal = { Surveys in Diff.\ Geom. }, Volume = { 1 }, Pages = { 201-241 }, Year = { 1991 } } @Incollection{ Sch93, Author = { R. Schoen }, Title = { {T}he role of harmonic mappings in rigidity and deformation problems }, Booktitle = { {C}omplex geometry ({O}saka 1990) }, Publisher = { Dekker }, Address = { New York }, Volume = { 143 }, Pages = { 179-200 }, Series = { Lecture Notes in Pure and Appl.\ Math. }, Year = { 1993 } } @Article{ SchSim81, Author = { R. Schoen and L. Simon }, Title = { {R}egularity of stable minimal hypersurfaces }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 34 }, Pages = { 741-797 }, Year = { 1981 } } @Article{ SchSim82, Author = { R. Schoen and L. Simon }, Title = { {A} new proof of the regularity theorem for rectifiable currents which minimize parametric elliptic functionals }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 31 }, Pages = { 415-434 }, Year = { 1982 } } @Incollection{ SchSim83, Author = { R. Schoen and L. Simon }, Title = { {R}egularity of simply connected surfaces with quasiconformal {G}auss maps }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 127-145 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Article{ SchSimYau75, Author = { R. Schoen and L. Simon and S.T. Yau }, Title = { {C}urvature estimates for stable minimal hypersurfaces }, Journal = { Acta Math. }, Volume = { 134 }, Pages = { 275-288 }, Year = { 1975 } } @Article{ SchUhl82, Author = { R. Schoen and K. Uhlenbeck }, Title = { {A} regularity theory for harmonic maps }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 307-335 }, Year = { 1982 } } @Article{ SchUhl83, Author = { R. Schoen and K. Uhlenbeck }, Title = { {B}oundary regularity and the {D}irichlet problem for harmonic maps }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 253-268 }, Year = { 1983 } } @Article{ SchUhl83A, Author = { R. Schoen and K. Uhlenbeck }, Title = { {A} regularity theory for harmonic maps (correction) }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 329 }, Year = { 1983 } } @Article{ SchUhl84, Author = { R. Schoen and K. Uhlenbeck }, Title = { {R}egularity of minimizing harmonic maps into the sphere }, Journal = { Invent.\ Math. }, Volume = { 78 }, Pages = { 89-100 }, Year = { 1984 } } @Incollection{ SchWolYau80, Author = { R. Schoen and S. Wolpert and S.T. Yau }, Title = { {G}eometric bounds on the low eigenvalue of a compact surface }, Booktitle = { {G}eometry of the {L}aplace operator }, Editor = { R. Osserman and A. Weinstein }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 36 }, Pages = { 279-285 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1980 } } @Misc{ SchWu, Author = { R. Schoen and H.H. Wu }, Title = { {O}n the {D}irichlet problem for manifolds of negative curvature } } @Article{ SchYau76, Author = { R. Schoen and S.T. Yau }, Title = { {H}armonic maps and the topology of stable hypersurfaces and manifolds of non-negative {R}icci curvature }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 51 }, Pages = { 333-341 }, Year = { 1976 } } @Article{ SchYau78, Author = { R. Schoen and S.T. Yau }, Title = { {I}ncompressible minimal surfaces, three dimensional manifolds with non-negative scalar curvature, and the positive mass conjecture in general relativity }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 75 }, Pages = { 2567 }, Year = { 1978 } } @Article{ SchYau78A, Author = { R. Schoen and S.T. Yau }, Title = { {O}n univalent harmonic maps between surfaces }, Journal = { Invent.\ Math. }, Volume = { 44 }, Pages = { 265-278 }, Year = { 1978 } } @Article{ SchYau79, Author = { R. Schoen and S.T. Yau }, Title = { {C}ompact group actions and the topology of manifolds with non-positive curvature }, Journal = { Topology }, Volume = { 18 }, Pages = { 361-380 }, Year = { 1979 } } @Article{ SchYau79A, Author = { R. Schoen and S.T. Yau }, Title = { {E}xistence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature }, Journal = { Ann.\ of Math. }, Volume = { 110 }, Pages = { 127-142 }, Year = { 1979 } } @Article{ SchYau79B, Author = { R. Schoen and S.T. Yau }, Title = { {O}n the proof of the positive mass conjecture in general relativity }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 65 }, Pages = { 45-76 }, Year = { 1979 } } @Article{ SchYau79C, Author = { R. Schoen and S.T. Yau }, Title = { {O}n the structure of manifolds with positive scalar curvature }, Journal = { Manuscripta Math. }, Volume = { 28 }, Pages = { 159-183 }, Year = { 1979 } } @Article{ SchYau79D, Author = { R. Schoen and S.T. Yau }, Title = { {P}ositivity of the total mass of a general space-time }, Journal = { Phys.\ Rev.\ Lett. }, Volume = { 43 }, Pages = { 1457-1459 }, Year = { 1979 } } @Article{ SchYau79E, Author = { R. Schoen and S.T. Yau }, Title = { {P}roof of the positive action conjecture in quantum relativity }, Journal = { Phys.\ Rev.\ Lett. }, Volume = { 42 }, Pages = { 547-548 }, Year = { 1979 } } @Article{ SchYau80, Author = { R. Schoen and S.T. Yau }, Title = { {T}he energy and linear momentum of space-times in general relativity }, Journal = { Comm.\ Math.\ Phys. }, Pages = { 179-200 }, Year = { 1980 } } @Article{ SchYau81, Author = { R. Schoen and S.T. Yau }, Title = { {T}he energy and linear momentum of space-times in general relativity }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 79 }, Pages = { 47-51 }, Year = { 1981 } } @Article{ SchYau81A, Author = { R. Schoen and S.T. Yau }, Title = { {O}n the proof of the positive mass conjecture }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 79 }, Pages = { 231-260 }, Year = { 1981 } } @Incollection{ SchYau82, Author = { R. Schoen and S.T. Yau }, Title = { {C}omplete three dimensional manifolds with positive {R}icci curvature and scalar curvature }, Booktitle = { {S}eminar on {D}ifferential {G}eometry }, Editor = { S.T. Yau }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton NJ }, Volume = { 102 }, Pages = { 209-228 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1982 } } @Article{ Sch88, Author = { V. Schroeder }, Title = { {E}xistence of immersed tori in manifolds of nonpositive curvature }, Journal = { J. Reine Angew.\ Math. }, Volume = { 390 }, Pages = { 32-46 }, Year = { 1988 } } @Article{ Sch86, Author = { G. Schumacher }, Title = { {H}armonic maps of the moduli space of compact {R}iemann surfaces }, Journal = { Math.\ Ann. }, Volume = { 275 }, Pages = { 455-466 }, Year = { 1986 } } @Article{ Sch87, Author = { K.H. Sch{\"u}ffler }, Title = { {F}unction theory and index theory for minimal surfaces of genus 1. {I}{I} {T}he index theorem for minimal surfaces of genus 1 }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 48 }, Pages = { 446-457 }, Year = { 1987 } } @Article{ Sch87A, Author = { K.H. Sch{\"u}ffler }, Title = { {F}unction theory and index theory for minimal surfaces of genus 1. {I}{I} {M}anifold structures for double periodic minimal surfaces }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 48 }, Pages = { 343-352 }, Year = { 1987 } } @Article{ Sch90, Author = { K.H. Sch{\"u}ffler }, Title = { {M}inimalfl{\"a}chen auf {M}{\"o}bius-{B}{\"a}ndern }, Journal = { Z. Anal.\ Anwendungen }, Volume = { 9 }, Pages = { 503-517 }, Year = { 1990 } } @Article{ Sch92, Author = { K.H. Sch{\"u}ffler }, Title = { {F}unktionentheoretische {M}ethoden in der {G}lobalanalysen der {M}inimalflachentheorie }, Journal = { Complex Variables Theory Appl. }, Volume = { 19 }, Pages = { 15-27 }, Year = { 1992 } } @Article{ Sci79, Author = { S. Sciuto }, Title = { {D}ifficulties in fixing the gauge in non-abelian gauge theories }, Journal = { Phys.\ Rep. }, Volume = { 49 }, Pages = { 181-191 }, Year = { 1979 } } @Article{ Sco83, Author = { P. Scott }, Title = { {T}he geometries of {$3$}-manifolds }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 15 }, Pages = { 401-487 }, Year = { 1983 } } @Misc{ Sea, Author = { H.C.J. Sealey }, Title = { {O}n harmonic maps of finite energy } } @Unpublished{ SeaA, Author = { H.C.J. Sealey }, Title = { {T}he stress-energy tensor and the vanishing of {${L}^2$}-harmonic forms }, Note = { preprint } } @Misc{ SeaB, Author = { H.C.J. Sealey }, Title = { {V}anishing theorems on manifolds diffeomorphic to {E}uclidean space with certian convexity and growth conditions } } @Unpublished{ Sea80, Author = { H.C.J. Sealey }, Title = { {S}ome properties of harmonic mappings }, Note = { Thesis, University of Warwick }, Year = { 1980 } } @Article{ Sea81, Author = { H.C.J. Sealey }, Title = { {H}armonic maps of small energy }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 13 }, Pages = { 405-408 }, Year = { 1981 } } @Article{ Sea81A, Author = { H.C.J. Sealey }, Title = { {O}n {C}heng's characterization of the {$2$}-sphere by eigenfunctions }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 13 }, Pages = { 403-404 }, Year = { 1981 } } @Incollection{ Sea82, Author = { H.C.J. Sealey }, Title = { {H}armonic diffeomorphisms of surfaces }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 140-145 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ Sea82A, Author = { H.C.J. Sealey }, Title = { {S}ome conditions insuring the vanishing of harmonic differential forms with applications to harmonic maps and {Y}ang--{M}ills theory }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 91 }, Pages = { 441-452 }, Year = { 1982 } } @Unpublished{ Sea82B, Author = { W.I. Seaman }, Title = { {H}ypersurfaces of constant mean curvature in {E}uclidean space and groups of {H}eisenberg type }, Note = { Thesis Univ. Massachussetts }, Year = { 1982 } } @Article{ Sea84, Author = { W.I. Seaman }, Title = { {H}elico{\"\i}ds of constant mean curvature and their {G}auss maps }, Journal = { Pacific J. Math. }, Volume = { 110 }, Pages = { 387-396 }, Year = { 1984 } } @Article{ Sea93, Author = { W.I. Seaman }, Title = { {O}n manifolds with nonnegative curvature on totally isotropic two-planes }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 338 }, Pages = { 843-855 }, Year = { 1993 } } @Article{ Seg79, Author = { G. Segal }, Title = { {T}he topology of spaces of rational functions }, Journal = { Acta Math. }, Volume = { 143 }, Pages = { 39-72 }, Year = { 1979 } } @Incollection{ Seg89, Author = { G. Segal }, Title = { {L}oop groups and harmonic maps }, Booktitle = { {A}dvances in homtopy theory ({C}ortona, 1988) }, Editor = { S.M. Salamon and B. Steer and W.A. Sutherland }, Publisher = { Camb.\ Univ.\ Press. }, Address = { Cambridge }, Volume = { 139 }, Pages = { 153-164 }, Series = { London Math.\ Soc.\ Lecture Note Ser. }, Year = { 1989 } } @Incollection{ Sei84, Author = { J.J. Seidel }, Title = { {H}armonics and combinatorics }, Booktitle = { {S}pecial {F}unctions }, Editor = { Askey }, Publisher = { Reidel }, Pages = { 287-307 }, Year = { 1984 } } @Misc{ Sek, Author = { K. Sekigawa }, Title = { {A}lmost hermitian structures on twistor bundles } } @Article{ SekVan89, Author = { K. Sekigawa and L. Vanhecke }, Title = { {H}armonic maps and {$s$}-regular manifolds }, Journal = { \v Casopis P\v est.\ Mat. }, Volume = { 114 }, Pages = { 391-398 }, Year = { 1989 } } @Misc{ Ser, Author = { T. Serbinowski }, Title = { {H}armonic maps into metric spaces with curvature bounded above } } @Article{ Ser94, Author = { T. Serbinowski }, Title = { {B}oundary regularity of harmonic maps to nonpositively curved metric spaces }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 2 }, Pages = { 1-15 }, Year = { 1994 } } @Article{ Ser73, Author = { V.G. Seretov }, Title = { {F}unctionals of {D}irichlet type and harmonic quasi-conformal mappings }, Journal = { Soviet Math.\ Dokl. }, Volume = { 14 }, Pages = { 551-554 }, Year = { 1973 } } @Article{ Ser74, Author = { V.G. Seretov }, Title = { {H}armonic mappings and univalent functions }, Journal = { Kuban Gos.\ Univ.\ Naucn.\ Trudy Vyp. }, Volume = { 180 }, Pages = { 143-153, 166-167 }, Year = { 1974 } } @Article{ Ser78, Author = { V.G. Seretov }, Title = { {E}xtremal quasi-conformal mappings with given boundary correspondence }, Journal = { Siberian Math.\ J. }, Volume = { 19 }, Pages = { 671-678 }, Year = { 1978 } } @Article{ Ser69, Author = { J. Serrin }, Title = { {O}n surfaces of constant mean curvature which... }, Journal = { Math.\ Z. }, Volume = { 112 }, Pages = { 77-88 }, Year = { 1969 } } @Article{ ShaYan90, Author = { J.P. Sha and D.G. Yang }, Title = { {O}n harmonic maps from conformal {${S}^{2n+1}$} to {${C}{P}^n$} }, Journal = { Amer.\ J. Math. }, Volume = { 112 }, Pages = { 1073-1078 }, Year = { 1990 } } @Article{ ShaZak79, Author = { A.B. Shabat and V.E. Zakharov }, Title = { {I}ntegration of nonlinear equations of mathematical physics by the method of inverse scattering {I}{I} }, Journal = { Functional Anal.\ Appl. }, Volume = { 13 }, Pages = { 166-174 }, Year = { 1979 } } @Article{ Sha84, Author = { D. Shapiro }, Title = { {P}roducts of sums of squares }, Journal = { Exposition.\ Math. }, Volume = { 2 }, Pages = { 235-261 }, Year = { 1984 } } @Article{ Sha88, Author = { J. Shatah }, Title = { {W}eak solutions and development of singularities of the {${S}{U}(2)$} {$\sigma$}-model }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 41 }, Pages = { 459-469 }, Year = { 1988 } } @Incollection{ Sha95, Author = { J. Shatah }, Title = { {T}he {C}auchy problem for harmonic maps on {M}inkowski space }, Booktitle = { {P}roceedings of the {I}nternational {C}ongress of {M}athematicians }, Publisher = { Birkh\"auser Verlag }, Address = { Basel }, Pages = { 1126-1132 }, Year = { 1995 } } @Misc{ ShaStr, Author = { J. Shatah and M. Struwe }, Title = { {R}egularity results for nonlinear wave equations } } @Article{ ShaTah92, Author = { J. Shatah and A. Tahvildar-Zadeh }, Title = { {R}egularity of harmonic maps from the {M}inkowski space into rotationally symmetric manifolds }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 45 }, Pages = { 947-971 }, Year = { 1992 } } @Article{ Sha85, Author = { W.T. Shaw }, Title = { {T}wistors, minimal surfaces and strings }, Journal = { Classical Quantum Gravity }, Volume = { 2 }, Pages = { L113-L119 }, Year = { 1985 } } @Article{ Sha86, Author = { W.T. Shaw }, Title = { {A}n ambitwistor description of bosonic or supersymmetric minimal surfaces and strings in {$4$} dimensions }, Journal = { Classical Quantum Gravity }, Volume = { 3 }, Pages = { 753-761 }, Year = { 1986 } } @Incollection{ Sha88A, Author = { W.T. Shaw }, Title = { {T}wistors and strings }, Booktitle = { {M}athematics and {G}eneral {R}elativity }, Editor = { J.A. Isenberg }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 71 }, Pages = { 337-363 }, Series = { Contemp.\ Math. }, Year = { 1988 } } @Article{ She84, Author = { C.L. Shen }, Title = { {A} generalization of the {S}chwarz--{A}hlfors lemma to the theory of harmonic maps }, Journal = { J. Reine Angew.\ Math. }, Volume = { 348 }, Pages = { 23-33 }, Year = { 1984 } } @Article{ She89, Author = { C.L. Shen }, Title = { {A} global pinching theorem of minimal hypersurfaces in the sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 105 }, Pages = { 192-198 }, Year = { 1989 } } @Incollection{ She89A, Author = { C.L. Shen }, Title = { {O}n the holomorphic maps from {R}iemann surfaces to {G}rassmannians }, Booktitle = { {D}ifferential {G}eometry and {T}opology ({T}ianjin 1986-87) }, Editor = { B. Jiang and C.K. Peng and Z. Hou }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1369 }, Pages = { 225-234 }, Series = { Lecture Notes in Math. }, Year = { 1989 } } @Article{ SheZho96, Author = { C.L. Shen and Q. Zhou }, Title = { {H}armonic maps and fundamental groups of nonpositively curved {R}iemannian manifolds }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 17 }, Pages = { 491--496 }, Year = { 1996 } } @Article{ She95, Author = { Y. Shen }, Title = { {A} {L}iouville theorem for harmonic maps }, Journal = { Amer.\ J. Math. }, Volume = { 117 }, Pages = { 773-785 }, Year = { 1995 } } @Misc{ She, Author = { Y.B. Shen }, Title = { {A} {L}iouville theorem for subharmonic functions and submanifolds with parallel mean curvature } } @Article{ She83, Author = { Y.B. Shen }, Title = { {T}otally real minimal submanifolds in a complex projective space }, Journal = { Kexue Tongbao }, Volume = { 28 }, Pages = { 1018-1021 }, Year = { 1983 } } @Article{ She84A, Author = { Y.B. Shen }, Title = { {O}n the tension field of the generalized {G}auss map }, Journal = { J. Hangzhou Univ. }, Volume = { 11 }, Pages = { 311-315 }, Note = { (Chinese with English summary) }, Year = { 1984 } } @Article{ She84B, Author = { Y.B. Shen }, Title = { {T}otally real {$n$}-dimensional minimal submanifolds in a complex {$n$}-dimensional projective space }, Journal = { Adv.\ in Math.\ (Beijing) }, Volume = { 13 }, Pages = { 65-70 }, Year = { 1984 } } @Article{ She85, Author = { Y.B. Shen }, Title = { {C}omplete submanifolds in {${E}^{n+p}$} with parallel mean curvature }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 6 }, Pages = { 345-350 }, Year = { 1985 } } @Article{ She85A, Author = { Y.B. Shen }, Title = { {O}n real minimal hypersurfaces in a complex projective space }, Journal = { Acta Math.\ Sinica }, Volume = { 28 }, Pages = { 85-90 }, Year = { 1985 } } @Article{ She86, Author = { Y.B. Shen }, Title = { {R}emarks on hypersurfaces with constant mean curvature in a higher dimensional pseudo-sphere }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 7 }, Pages = { 483-487 }, Year = { 1986 } } @Article{ She88, Author = { Y.B. Shen }, Title = { {C}urvature and stability for minimal submanifolds }, Journal = { Sci.\ Sinica }, Volume = { 31 }, Pages = { 787-797 }, Year = { 1988 } } @Article{ She89B, Author = { Y.B. Shen }, Title = { {O}n intrinsic rigidity for minimal submanifolds in a sphere }, Journal = { Sci.\ in China }, Volume = { 32 }, Pages = { 769-781 }, Year = { 1989 } } @Article{ She90, Author = { Y.B. Shen }, Title = { {H}armonic {G}auss maps and {C}odazzi tensor for affine hypersurfaces }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 55 }, Pages = { 298-305 }, Year = { 1990 } } @Article{ She92, Author = { Y.B. Shen }, Title = { {C}urvature pinching for three-dimensional minimal submanifolds in a sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 115 }, Pages = { 791-795 }, Year = { 1992 } } @Incollection{ She93, Author = { Y.B. Shen }, Title = { {O}n conformal superminimal immersions of surfaces into {${C}{P}^n$} }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 457-463 }, Year = { 1993 } } @Article{ She93A, Author = { Y.B. Shen }, Title = { {T}otally real minimal submanifolds in a quaternionic projective space }, Journal = { Chinese Ann.\ Math.\ Ser.\ B }, Volume = { 14 }, Pages = { 297-306 }, Year = { 1993 } } @Article{ She95A, Author = { Y.B. Shen }, Title = { {A} {L}iouville theorem for harmonic maps }, Journal = { Amer.\ J. Math. }, Volume = { 117 }, Pages = { 773-785 }, Year = { 1995 } } @Unpublished{ SheA, Author = { Y.S. Shen }, Title = { {O}n submanifolds in {R}iemannian manifolds of constant curvature }, Note = { preprint } } @Incollection{ ShiYau94, Author = { W. Shi and S.T. Yau }, Title = { {H}armonic maps on complete noncompact {R}iemannian manifolds }, Booktitle = { {A} tribute to {I}lya {B}akelman ({C}ollege {S}tation, {T}{X}, 1993) }, Publisher = { Texas A \& M Univ. }, Address = { College Station, TX }, Volume = { 3 }, Pages = { 79--120 }, Series = { Discourses Math.\ Appl. }, Year = { 1994 } } @Article{ Shi63, Author = { K. Shibata }, Title = { {O}n the existence of a harmonic mapping }, Journal = { Osaka J. Math. }, Volume = { 15 }, Pages = { 173-211 }, Year = { 1963 } } @Article{ Shi81, Author = { K. Shibata }, Title = { {Q}uasiconformal mappings in {${\bf {R}}^n$} with their application to a problem of minimal surfaces }, Journal = { Osaka J. Math. }, Volume = { 18 }, Pages = { 643-667 }, Year = { 1981 } } @Article{ Shi39, Author = { M. Shiffman }, Title = { {T}he {P}lateau problem for minimal surfaces of arbitrary topological structure }, Journal = { Amer.\ J. Math. }, Volume = { 61 }, Pages = { 853-882 }, Year = { 1939 } } @Article{ Shi39A, Author = { M. Shiffman }, Title = { {T}he {P}lateau problem for non-relative minima }, Journal = { Ann.\ of Math. }, Volume = { 40 }, Pages = { 834-854 }, Year = { 1939 } } @Article{ Shi42, Author = { M. Shiffman }, Title = { {U}nstable minimal surfaces with several boundaries }, Journal = { Ann.\ of Math. }, Volume = { 43 }, Pages = { 197-222 }, Year = { 1942 } } @Article{ Shi71, Author = { K. Shiga }, Title = { {O}n holomorphic extension from the boundary }, Journal = { Nagoya Math.\ J. }, Volume = { 42 }, Pages = { 57-66 }, Year = { 1971 } } @Article{ Shi82, Author = { K. Shiga }, Title = { {A}n application of harmonic mapping to complex analytic geometry }, Journal = { Bull.\ Fac.\ Gen.\ Ed.\ Gifu Univ. }, Volume = { 17 }, Pages = { 57-60 }, Year = { 1982 } } @Article{ Shi95, Author = { H. Shima }, Title = { {H}armonicity of gradient mappings of level surfaces in a real affine space }, Journal = { Geom.\ Dedicata }, Volume = { 56 }, Pages = { 177-184 }, Year = { 1995 } } @Article{ Shi92, Author = { H.Y. Shin }, Title = { {D}egree {$1$} singularities of energy minimizing maps to a bumpy sphere }, Journal = { Math.\ Ann. }, Volume = { 293 }, Pages = { 509-521 }, Year = { 1992 } } @Article{ Shi85, Author = { K. Shiohama }, Title = { {T}otal curvatures and minimal areas of complete surfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 94 }, Pages = { 310-316 }, Year = { 1985 } } @Article{ ShiTak70, Author = { K. Shiohama and R. Takagi }, Title = { {A} characterization of a standard torus in {${E}^3$} }, Journal = { J. Differential Geom. }, Volume = { 4 }, Pages = { 477-485 }, Year = { 1970 } } @Article{ Sha93, Author = { U. Sh{\"a}per }, Title = { {G}eodesics on loop spaces }, Journal = { J. Geom.\ Phys. }, Volume = { 11 }, Pages = { 553-557 }, Year = { 1993 } } @Article{ Sid89, Author = { T. Sideris }, Title = { {G}lobal existence of harmonic maps in {M}inkowski space }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 42 }, Pages = { 1-13 }, Year = { 1989 } } @Misc{ Sim, Author = { L. Simon }, Title = { {O}n the singularities of harmonic maps } } @Unpublished{ SimA, Author = { L. Simon }, Title = { {S}ingularities of geometric variational problems }, Address = { Stanford }, Note = { Grad. Summer School Lectures } } @Misc{ SimB, Author = { L. Simon }, Title = { {U}niqueness of some cylindrical tangent cones } } @Article{ Sim76, Author = { L. Simon }, Title = { {R}emarks on curvature estimates for minimal hypersurfaces }, Journal = { Duke Math.\ J. }, Volume = { 43 }, Pages = { 545-553 }, Year = { 1976 } } @Article{ Sim82, Author = { L. Simon }, Title = { {I}solated singularities of minimal surfaces }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 1 }, Pages = { 70-100 }, Year = { 1982 } } @Article{ Sim83, Author = { L. Simon }, Title = { {A}symptotics for a class of non-linear evolution equations, with applications to geometric problems }, Journal = { Ann.\ of Math. }, Volume = { 118 }, Pages = { 525-571 }, Year = { 1983 } } @Misc{ Sim83A, Author = { L. Simon }, Title = { {L}ectures on geometric measure theory }, Volume = { 3 }, Series = { Proc.\ Cent.\ Math.\ Austral.\ Nat.\ Univ. }, Year = { 1983 } } @Incollection{ Sim83B, Author = { L. Simon }, Title = { {S}urvey lectures on minimal submanifolds }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 3-52 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Article{ Sim84, Author = { L. Simon }, Title = { {I}solated singularities for extrema of geometric variational problems }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 8 }, Pages = { 46-50 }, Year = { 1984 } } @Incollection{ Sim84A, Author = { L. Simon }, Title = { {R}ecent developments in the theory of minimal surfaces }, Booktitle = { {P}roc. {I}ntern. {C}ong. {M}ath. {W}arsaw 1983 }, Publisher = { PWN }, Address = { Warsaw }, Pages = { 579-584 }, Year = { 1984 } } @Article{ Sim85, Author = { L. Simon }, Title = { {E}xistence of {W}illmore surfaces }, Journal = { Proc.\ Centre Math.\ Anal.\ Austral.\ Nat.\ Univ. }, Volume = { 10 }, Pages = { 187-216 }, Year = { 1985 } } @Incollection{ Sim85A, Author = { L. Simon }, Title = { {I}solated singularities of extrema of geometric variational problems }, Booktitle = { {H}armonic mappings and minimal immersions }, Editor = { E. Giusti }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1161 }, Pages = { 206-277 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Incollection{ Sim86, Author = { L. Simon }, Title = { {A}symptotic behaviour of minimal submanifolds and harmonic maps }, Booktitle = { {G}eometric measure theory and the calculus of variations }, Editor = { W.K. Allard and F.J. Almgren }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 44 }, Pages = { 369-377 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Article{ Sim89, Author = { L. Simon }, Title = { {E}ntire solutions of the minimal surface equation }, Journal = { J. Differential Geom. }, Volume = { 30 }, Pages = { 643-688 }, Year = { 1989 } } @Incollection{ Sim92, Author = { L. Simon }, Title = { {T}he singular set of minimal submanifolds and harmonic maps }, Booktitle = { {P}rogress in {P}artial {D}ifferential {E}quations: {C}alculus of {V}ariations, {A}pplications }, Publisher = { Longman Sci.\ Tech. }, Address = { Harlow }, Volume = { 267 }, Pages = { 99-108 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1992 } } @Article{ Sim93, Author = { L. Simon }, Title = { {C}ylindrical tangent cones and the singular set of minimal submanifolds }, Journal = { J. Differential Geom. }, Volume = { 38 }, Pages = { 585-652 }, Year = { 1993 } } @Article{ Sim93A, Author = { L. Simon }, Title = { {E}xistence of surfaces minimizing the {W}illmore functional }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 1 }, Pages = { 281-326 }, Year = { 1993 } } @Article{ Sim93B, Author = { L. Simon }, Title = { {R}ectifiability of the singular sets of multiplicity {$1$} minimal surfaces and energy minimizing maps }, Publisher = { Internat.\ Press }, Address = { Cambridge, MA }, Journal = { Surveys in Diff.\ Geom. }, Volume = { 2 }, Pages = { 246-305 }, Year = { 1993 } } @Incollection{ Sim93C, Author = { L. Simon }, Title = { {T}heorems on the regularity and singularity of minimal surfaces and harmonic maps }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 111-145 }, Year = { 1993 } } @Article{ Sim95, Author = { L. Simon }, Title = { {R}ectifiability of the singular set of energy minimizing maps }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 3 }, Pages = { 1-65 }, Year = { 1995 } } @Book{ Sim96, Author = { L. Simon }, Title = { {T}heorems on regularity and singularity of energy minimizing maps }, Publisher = { Birkh\"auser Verlag }, Address = { Basel }, Series = { ETH Lectures in Mathematics }, Year = { 1996 } } @Misc{ SimSmi, Author = { L. Simon and F.R. Smith }, Title = { {O}n the existence of embedded minimal 2-spheres in the 3-sphere endowed with an arbitrary metric } } @Article{ SimSol86, Author = { L. Simon and B. Solomon }, Title = { {M}inimal hypersurfaces asymptotic to quadratic cones in {${\bf {R}}^{n+1}$} }, Journal = { Invent.\ Math. }, Volume = { 86 }, Pages = { 535-551 }, Year = { 1986 } } @Article{ SimC, Author = { U. Simon }, Title = { {I}sometries with spheres }, Journal = { Math.\ Z. } } @Article{ Sim77, Author = { U. Simon }, Title = { {S}ubmanifolds with parallel mean curvature vector and the curvature of minimal submanifolds of spheres }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 29 }, Pages = { 106-112 }, Year = { 1977 } } @Article{ Sim68, Author = { J. Simons }, Title = { {M}inimal varieties in {R}iemannian manifolds }, Journal = { Ann.\ of Math. }, Volume = { 88 }, Pages = { 62-105 }, Year = { 1968 } } @Article{ Sim88, Author = { C.T. Simpson }, Title = { {C}onstructing variations of {H}odge structure using {Y}ang-{M}ills theory and applications to uniformization }, Journal = { J. Amer.\ Math.\ Soc. }, Volume = { 1 }, Pages = { 867-918 }, Year = { 1988 } } @Article{ Sim90, Author = { C.T. Simpson }, Title = { {H}armonic bundles on noncompact curves }, Journal = { J. Amer.\ Math.\ Soc. }, Volume = { 3 }, Pages = { 713-770 }, Year = { 1990 } } @Unpublished{ Sim90A, Author = { C.T. Simpson }, Title = { {T}he ubiquity of variations of {H}odge structure }, Note = { Preprint }, Year = { 1990 } } @Article{ Sim92A, Author = { C.T. Simpson }, Title = { {H}iggs bundles and local systems }, Journal = { Inst.\ Hautes \'Etudes Sci.\ Publ.\ Math. }, Volume = { 75 }, Pages = { 5-95 }, Year = { 1992 } } @Article{ Sin60, Author = { I.M. Singer }, Title = { {I}nfinitesimally homogeneous spaces }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 13 }, Pages = { 685-697 }, Year = { 1960 } } @Incollection{ Siu, Author = { Y.T. Siu }, Title = { {C}omplex-analycity of harmonic maps and vanishing theorems }, Booktitle = { {S}everal {C}omplex {V}ariables ({H}angzhou 1981) }, Editor = { J.J. Kohn and Q.K. Lu and R. Remmert and Y.T. Siu }, Publisher = { Birkha\"user }, Address = { Boston }, Pages = { 73-84 } } @Article{ Siu79, Author = { Y.T. Siu }, Title = { {T}he complex-analyticity of harmonic maps and the strong rigidity of compact {K}\"ahler manifolds }, Journal = { Proc.\ Nat.\ Acad.\ Sci.\ U.S.A. }, Volume = { 76 }, Pages = { 2107-2108 }, Year = { 1979 } } @Article{ Siu79A, Author = { Y.T. Siu }, Title = { {S}ome remarks on the complex analyticity of harmonic maps }, Journal = { Southeast Asian Bull.\ Math. }, Volume = { 3 }, Pages = { 240-253 }, Year = { 1979 } } @Article{ Siu80, Author = { Y.T. Siu }, Title = { {T}he complex-analyticity of harmonic maps and the strong rigidity of compact {K}\"ahler manifolds }, Journal = { Ann.\ of Math. }, Volume = { 112 }, Pages = { 73-111 }, Year = { 1980 } } @Article{ Siu80A, Author = { Y.T. Siu }, Title = { {C}urvature characterization of hyperquadrics }, Journal = { Duke Math.\ J. }, Volume = { 47 }, Pages = { 641-654 }, Year = { 1980 } } @Article{ Siu81, Author = { Y.T. Siu }, Title = { {S}trong rigidity of compact quotients of exceptional bounded symmetric domains }, Journal = { Duke Math.\ J. }, Volume = { 48 }, Pages = { 857-871 }, Year = { 1981 } } @Article{ Siu82, Author = { Y.T. Siu }, Title = { {C}omplex analyticity of harmonic maps, vanishing and {L}efschetz theorems }, Journal = { J. Differential Geom. }, Volume = { 17 }, Pages = { 55-138 }, Year = { 1982 } } @Incollection{ Siu83, Author = { Y.T. Siu }, Title = { {S}ome recent developments in complex differential geometry }, Booktitle = { {P}roc. {I}.{C}.{M}. {W}arsaw }, Pages = { 287-297 }, Year = { 1983 } } @Incollection{ Siu85, Author = { Y.T. Siu }, Title = { {S}ome recent results in complex manifold theory related to vanishing theorems for the semipositive case }, Booktitle = { {A}rbeitstagung {B}onn 1984 }, Editor = { F. Hirzebruch and J. Schwermer and S. Suter }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1111 }, Pages = { 169-192 }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Incollection{ Siu87, Author = { Y.T. Siu }, Title = { {S}trong rigidity for {K}\"ahler manifolds and the construction of bounded holomorphic functions }, Booktitle = { {D}iscrete groups in geometry }, Publisher = { Birkh\"auser }, Address = { Boston }, Pages = { 124-151 }, Year = { 1987 } } @Incollection{ Siu93, Author = { Y.T. Siu }, Title = { {G}eometric superrigidity }, Booktitle = { {A}lgebraic geometry and related topics }, Editor = { J.H. Yang }, Publisher = { Internat.\ Press }, Address = { Cambridge, MA }, Volume = { 1 }, Pages = { 105-119 }, Series = { Lect.\ Notes Algebr.\ Geom. }, Year = { 1993 } } @Article{ SiuYau77, Author = { Y.T. Siu and S.T. Yau }, Title = { {C}omplete {K}\"ahler manifolds with nonpositive curvature of faster than quadratic decay }, Journal = { Ann.\ of Math. }, Volume = { 105 }, Pages = { 225-264 }, Year = { 1977 } } @Article{ SiuYau80, Author = { Y.T. Siu and S.T. Yau }, Title = { {C}ompact {K}\"ahler manifolds of positive bisectional curvature }, Journal = { Invent.\ Math. }, Volume = { 59 }, Pages = { 189-204 }, Year = { 1980 } } @Misc{ SiuYeu, Author = { Y.T. Siu and S.K. Yeung }, Title = { {G}eometric superrigidity for certain real locally symmetric manifolds } } @Article{ Sma87, Author = { N. Smale }, Title = { {A} bridge principle for minimal and constant mean curvature submanifolds of {${\bf {R}}^n$} }, Journal = { Invent.\ Math. }, Volume = { 90 }, Pages = { 505-549 }, Year = { 1987 } } @Article{ Sma89, Author = { N. Smale }, Title = { {M}inimal hypersurfaces with many isolated singularities }, Journal = { Ann.\ of Math. }, Volume = { 130 }, Pages = { 603-642 }, Year = { 1989 } } @Unpublished{ Sma92, Author = { N. Smale }, Title = { {A}n equivariant construction of minimal surfaces with non trivial singular sets }, Note = { IHES preprint }, Year = { 1992 } } @Article{ Sma93, Author = { N. Smale }, Title = { {G}eometric partial differential equations with isolated singularities }, Journal = { J. Reine Angew.\ Math. }, Volume = { 440 }, Pages = { 1-43 }, Year = { 1993 } } @Article{ Sma65, Author = { S. Smale }, Title = { {O}n the {M}orse index theorem }, Journal = { J. Math.\ Mech. }, Volume = { 14 }, Pages = { 1049-1055 }, Year = { 1965 } } @Misc{ Sma, Author = { A.J. Small }, Title = { {D}uality for {C}alabi curves and minimal surfaces in {${\bf {R}}^n$} } } @Misc{ SmaA, Author = { A.J. Small }, Title = { {M}inimal surfaces in {${\bf {R}}^4$} and the {K}lein correspondence } } @Misc{ SmaB, Author = { A.J. Small }, Title = { {M}onopole charge, null curves and jumping lines } } @Misc{ SmaC, Author = { A.J. Small }, Title = { {N}ull curves in self-dual {E}instein manifolds and {E}instein-{W}eyl spaces } } @Misc{ SmaD, Author = { A.J. Small }, Title = { {W}eierstrass formulae for surfaces of constant mean curvature {$1$} in {${\bf {H}}^3$} } } @Unpublished{ Sma88, Author = { A.J. Small }, Title = { {A} twistorial interpretation of the {W}eierstrass representation formulae }, Note = { PhD Thesis, Warwick }, Year = { 1988 } } @Unpublished{ Sma90, Author = { A.J. Small }, Title = { {T}he twistorial construction of null holomorphic curves in {${\bf {C}}^3$} }, Note = { Preprint, MPI Bonn }, Year = { 1990 } } @Article{ Sma92A, Author = { A.J. Small }, Title = { {M}inimal surfaces in {${\bf {R}}^3$} and algebraic curves }, Journal = { Diff.\ Geom.\ Appl. }, Volume = { 2 }, Pages = { 369-384 }, Year = { 1992 } } @Article{ Sma94, Author = { A.J. Small }, Title = { {L}inear structures on the collections of minimal surfaces in {${\bf {R}}^3$} and {${\bf {R}}^4$} }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 12 }, Pages = { 97-101 }, Year = { 1994 } } @Article{ Sma94A, Author = { A.J. Small }, Title = { {S}urfaces of constant mean curvature {$1$} in {${\bf {H}}^3$} and algebraic curves on a quadric }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 122 }, Pages = { 1211-1220 }, Year = { 1994 } } @Unpublished{ Smi82, Author = { F.R. Smith }, Title = { {O}n the existence of embedded minimal {$2$}-spheres in the {$3$}-sphere, endowed with an arbitrary metric }, Note = { University of Melbourne Ph.D Thesis }, Year = { 1982 } } @Article{ Smi86, Author = { P.A.N. Smith }, Title = { {C}ounterexample to smoothing convex functions }, Journal = { Canad.\ Math.\ Bull. }, Volume = { 29 }, Pages = { 308-313 }, Year = { 1986 } } @Unpublished{ Smi72, Author = { R.T. Smith }, Title = { {H}armonic mappings of spheres }, Note = { Thesis, Warwick University }, Year = { 1972 } } @Article{ Smi72A, Author = { R.T. Smith }, Title = { {H}armonic mappings of spheres }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 78 }, Pages = { 593-596 }, Year = { 1972 } } @Article{ Smi74, Author = { R.T. Smith }, Title = { {T}he spherical representations of groups transitive on {${S}^n$} }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 24 }, Pages = { 307-325 }, Year = { 1974 } } @Article{ Smi75, Author = { R.T. Smith }, Title = { {H}armonic mappings of spheres }, Journal = { Amer.\ J. Math. }, Volume = { 97 }, Pages = { 364-385 }, Year = { 1975 } } @Article{ Smi75A, Author = { R.T. Smith }, Title = { {T}he second variation formula for harmonic mappings }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 47 }, Pages = { 229-236 }, Year = { 1975 } } @Misc{ Smy, Author = { B. Smyth }, Title = { {T}he {G}auss map in abelian varieties } } @Misc{ SmyA, Author = { B. Smyth }, Title = { {T}he generalization of {D}elaunay's theorem to constant mean curvature surfaces with continuous internal symmetry } } @Unpublished{ SmyB, Author = { B. Smyth }, Title = { {T}he geometry of bounded solutions of the sinh-{G}ordon equation }, Note = { preprint } } @Article{ Smy73, Author = { B. Smyth }, Title = { {S}ubmanifolds of constant mean curvature }, Journal = { Math.\ Ann. }, Volume = { 205 }, Pages = { 265-280 }, Year = { 1973 } } @Article{ Smy76, Author = { B. Smyth }, Title = { {W}eakly ample {K}\"ahler manifolds and {E}uler number }, Journal = { Math.\ Ann. }, Volume = { 224 }, Pages = { 269-279 }, Year = { 1976 } } @Incollection{ Smy83, Author = { B. Smyth }, Title = { {M}inimal surfaces and {W}eyl groups }, Booktitle = { {D}ifferential {G}eometry and {M}athematical {P}hysics }, Editor = { M. Cahen and M. de~Wilde and L. Lemaire and L. Vanhecke }, Publisher = { Reidel }, Address = { Dortrecht, Holland, London }, Volume = { 3 }, Series = { Math.\ Phys.\ Stud. }, Year = { 1983 } } @Article{ Smy84, Author = { B. Smyth }, Title = { {S}tationary minimal surfaces with boundary on a simplex }, Journal = { Invent.\ Math. }, Volume = { 76 }, Pages = { 411-420 }, Year = { 1984 } } @Article{ SmyXav92, Author = { B. Smyth and F. Xavier }, Title = { {A} sharp geometric estimate for the index of an umbilic on a smooth surface }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 24 }, Pages = { 176-180 }, Year = { 1992 } } @Article{ SmyWei, Author = { R.W. Smyth and T. Weinstein }, Title = { {C}onformally homeomorphic {L}orentz surfaces need not be conformally diffeomorphic }, Journal = { Proc.\ Amer.\ Math.\ Soc. } } @Misc{ SmyWeiA, Author = { R.W. Smyth and T. Weinstein }, Title = { {H}ow many {L}orentz surfaces are there ? } } @Article{ Sol84, Author = { B. Solomon }, Title = { {O}n the {G}auss map of an area-minimizing hypersurface }, Journal = { J. Differential Geom. }, Volume = { 19 }, Pages = { 221-232 }, Year = { 1984 } } @Article{ Sol85, Author = { B. Solomon }, Title = { {H}armonic mappings to spheres }, Journal = { J. Differential Geom. }, Volume = { 21 }, Pages = { 151-162 }, Year = { 1985 } } @Article{ Sol86, Author = { B. Solomon }, Title = { {O}n foliation of {${\bf {R}}^{n+1}$} by minimal hypersurfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 61 }, Pages = { 67-83 }, Year = { 1986 } } @Article{ Son92, Author = { R.X. Song }, Title = { {T}otal geodesicity and non-existence of harmonic maps }, Journal = { J. Hangzhou Univ. }, Volume = { 19 }, Pages = { 231-239 }, Note = { (Chinese) }, Year = { 1992 } } @Article{ Son92A, Author = { S.Y. Song }, Title = { {L}evel isometric mappings and {G}auss mappings }, Journal = { Acta Math.\ Sci. }, Volume = { 12 }, Pages = { 199-206 }, Note = { (Chinese) }, Year = { 1992 } } @Article{ Soy89, Author = { A. Soyeur }, Title = { {T}he {D}irichlet problem for harmonic maps from the disc into the {$2$}-sphere }, Journal = { Proc.\ Roy.\ Soc.\ Edinburgh Sect.\ A }, Volume = { 113 }, Pages = { 229-234 }, Year = { 1989 } } @Article{ Soy90, Author = { A. Soyeur }, Title = { {A} global existence result for the heat flow of harmonic maps }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 15 }, Pages = { 237-244 }, Year = { 1990 } } @Article{ Spe86, Author = { D. Spector }, Title = { {I}ntegrability of nonlinear sigma models }, Journal = { Phys.\ Lett.\ B }, Volume = { 171 }, Pages = { 231-234 }, Year = { 1986 } } @Unpublished{ Spe82, Author = { E. Sperner }, Title = { {A} priori gradient estimates for harmonic mappings }, Note = { preprint, University of Bonn }, Year = { 1982 } } @Misc{ Spr, Author = { J. Spruck }, Title = { {T}he elliptic sinh {G}ordon equation and the construction of toroidal soap bubbles } } @Article{ Spr75, Author = { J. Spruck }, Title = { {R}emarks on the stability of minimal submanifolds of {${\bf {R}}^n$} }, Journal = { Math.\ Z. }, Volume = { 144 }, Pages = { 169-174 }, Year = { 1975 } } @Article{ Sta90, Author = { S. Stafford }, Title = { {A} probabilistic proof of {S}.-{Y}.{C}heng's {L}iouville theorem }, Journal = { Ann.\ Probab. }, Volume = { 18 }, Pages = { 1816-1822 }, Year = { 1990 } } @Unpublished{ Ste, Author = { K. Steffen }, Title = { {O}n the nonuniqueness of surfaces with prescribed constant mean curvature spanning a given contour }, Note = { preprint } } @Article{ Ste72, Author = { K. Steffen }, Title = { {E}in verbesserter {E}xistenzsatz f\"ur {F}l\"achen konstanter mittlerer {K}r\"ummung }, Journal = { Manuscripta Math. }, Volume = { 6 }, Pages = { 105-139 }, Year = { 1972 } } @Article{ Ste72A, Author = { K. Steffen }, Title = { {F}l\"achen konstanter mittlerer {K}r\"ummung mit vorgegebenem volumen oder flacheninhalt }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 49 }, Pages = { 99-128 }, Year = { 1972 } } @Article{ Ste76, Author = { K. Steffen }, Title = { {I}soperimetric inequalities... }, Journal = { Math.\ Ann. }, Volume = { 222 }, Pages = { 97-144 }, Year = { 1976 } } @Article{ Ste76A, Author = { K. Steffen }, Title = { {O}n the existence... }, Journal = { Math.\ Z. }, Volume = { 146 }, Pages = { 113-135 }, Year = { 1976 } } @Incollection{ Ste90, Author = { K. Steffen }, Title = { {H}armonic maps with free boundaries }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 343-357 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Misc{ Ste91, Author = { K. Steffen }, Title = { {A}n introduction to harmonic mappings }, Address = { Bonn }, Series = { Vorlesungsreihe SFB 256 }, Year = { 1991 } } @Article{ Ste95, Author = { S.E. Stepanov }, Title = { {O}n the global theory of some classes of mappings }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 13 }, Pages = { 239-249 }, Year = { 1995 } } @Article{ Ste87, Author = { I. Sterling }, Title = { {N}ew examples of imbedded spherical soap bubbles in {${S}^{N}(1)$} }, Journal = { Manuscripta Math. }, Volume = { 59 }, Pages = { 277-294 }, Year = { 1987 } } @Incollection{ Ste91A, Author = { I. Sterling }, Title = { {C}onstant mean curvature tori }, Booktitle = { {G}eometric {A}nalysis and {C}omputer {G}raphics }, Editor = { P. Concus and R. Finn and D.A. Hoffman }, Publisher = { Springer }, Address = { Berlin }, Volume = { 17 }, Pages = { 175-180 }, Series = { MSRI Publ. }, Year = { 1991 } } @Article{ SteWen93, Author = { I. Sterling and H.C. Wente }, Title = { {E}xistence and classification of constant mean curvature multibubbletons of finite and infinite type }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 42 }, Pages = { 1239-1266 }, Year = { 1993 } } @Unpublished{ SteWen93A, Author = { I. Sterling and H.C. Wente }, Title = { {R}enormalized energy for multisolitons and the {L}anger-{P}erline invariant }, Note = { Preprint }, Year = { 1993 } } @Incollection{ Sto83, Author = { W.R. Stoeger }, Title = { {R}osen's bi-metric theory of gravity as a harmonic map }, Booktitle = { {P}roc. third {M}. {G}rossmann {M}eeting {R}ec. {D}ev. {G}en. {R}el. }, Publisher = { North Holland }, Pages = { 921-925 }, Year = { 1983 } } @Article{ StoZak87, Author = { I. Stokoe and W.J. Zakrzewski }, Title = { {D}ynamics of solutions of the {${C}{P}^{({N}-1)}$} models in {$(2+1)$} dimensions }, Journal = { Z. Phys.\ C }, Volume = { 34 }, Pages = { 491-496 }, Year = { 1987 } } @Incollection{ Sto77, Author = { R. Stora }, Title = { {Y}ang--{M}ills instantons, geometrical aspects }, Booktitle = { {P}roc. {S}chool. {M}ath. {P}hys. {E}rice }, Year = { 1977 } } @Incollection{ Sto88, Author = { R. Stora }, Title = { ``{C}omplex'' harmonic maps from {${S}^2$} to {${C}{P}^{N}$} }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 224-231 }, Year = { 1988 } } @Article{ Str75, Author = { P. Stredder }, Title = { {N}atural differential operators on {R}iemannian manifolds and representations of the orthogonal and special orthogonal groups }, Journal = { J. Differential Geom. }, Volume = { 10 }, Pages = { 647-660 }, Year = { 1975 } } @Article{ Str80, Author = { G.O. Stromer }, Title = { {I}nstabile {M}inimalflachen in {R}iemannschen {M}annigfaltigkeiten nichtpositiver {S}chnittkrummung }, Journal = { J. Reine Angew.\ Math. }, Volume = { 315 }, Pages = { 16-39 }, Year = { 1980 } } @Misc{ Str, Author = { M. Struwe }, Title = { {B}oundary regularity for the evolution of harmonic maps } } @Unpublished{ StrA, Author = { M. Struwe }, Title = { {A} counterexample in regularity for parabolic systems }, Note = { preprint } } @Misc{ StrB, Author = { M. Struwe }, Title = { {T}he evolution of harmonic maps ({P}art {I}) } } @Misc{ StrC, Author = { M. Struwe }, Title = { {F}ree boundary problems for surfaces of prescribed mean curvature and harmonic maps } } @Misc{ StrD, Author = { M. Struwe }, Title = { {M}ultiple solutions to the {D}irichlet problem for the equation of prescribed mean curvature } } @Unpublished{ StrE, Author = { M. Struwe }, Title = { {T}he {Y}ang--{M}ills flow in four dimensions }, Note = { preprint } } @Article{ Str81, Author = { M. Struwe }, Title = { {T}he existence of surfaces of constant mean curvature with free boundaries }, Journal = { Acta Math. }, Volume = { 160 }, Pages = { 19-64 }, Year = { 1981 } } @Article{ Str82, Author = { M. Struwe }, Title = { {M}ultiple solutions of differential equations without the {P}alais--{S}male condition }, Journal = { Math.\ Ann. }, Volume = { 261 }, Pages = { 399-412 }, Year = { 1982 } } @Unpublished{ Str84, Author = { M. Struwe }, Title = { {A} {M}orse theory for annulus-type minimal surfaces }, Note = { Bonn preprint }, Year = { 1984 } } @Article{ Str84A, Author = { M. Struwe }, Title = { {O}n a critical point theory for minimal surfaces spanning a wire in {${\bf {R}}^n$} }, Journal = { J. Reine Angew.\ Math. }, Volume = { 349 }, Pages = { 1-23 }, Year = { 1984 } } @Article{ Str84B, Author = { M. Struwe }, Title = { {O}n a free boundary problem for minimal surfaces }, Journal = { Invent.\ Math. }, Volume = { 75 }, Pages = { 547-560 }, Year = { 1984 } } @Article{ Str85, Author = { M. Struwe }, Title = { {F}unctional analytic aspects of the {P}lateau problem }, Journal = { Delft Progr.\ Rep. }, Volume = { 10 }, Pages = { 271-281 }, Year = { 1985 } } @Article{ Str85A, Author = { M. Struwe }, Title = { {L}arge {${H}$}-surfaces via the mountain-pass lemma }, Journal = { Math.\ Ann. }, Volume = { 270 }, Pages = { 441-495 }, Year = { 1985 } } @Article{ Str85B, Author = { M. Struwe }, Title = { {O}n the evolution of harmonic mappings of {R}iemannian surfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 60 }, Pages = { 558-581 }, Year = { 1985 } } @Incollection{ Str86, Author = { M. Struwe }, Title = { {A} generalized {P}alais--{S}male condition and applications }, Booktitle = { {N}onlinear functional analysis and its applications }, Editor = { F.E. Browder }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 45 }, Pages = { 401-411 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Article{ Str86A, Author = { M. Struwe }, Title = { {N}onuniqueness in the {P}lateau {P}roblem for surfaces of constant mean curvature }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 93 }, Pages = { 135-157 }, Year = { 1986 } } @Article{ Str88, Author = { M. Struwe }, Title = { {T}he existence of surfaces of constant mean curvature with free boundaries }, Journal = { Acta Math. }, Volume = { 160 }, Pages = { 19-64 }, Year = { 1988 } } @Incollection{ Str88A, Author = { M. Struwe }, Title = { {H}eat flow methods for harmonic maps of surfaces and applications to free boundary problems }, Booktitle = { {P}artial {D}ifferential {E}quations }, Editor = { F.A. Cardoso and D.G. de~Fiqueiredo and R. Iorio and O. Lopes }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1324 }, Pages = { 293-319 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Article{ Str88B, Author = { M. Struwe }, Title = { {O}n the evolution of harmonic maps in higher dimensions }, Journal = { J. Differential Geom. }, Volume = { 28 }, Pages = { 485-502 }, Year = { 1988 } } @Book{ Str88C, Author = { M. Struwe }, Title = { {P}lateau's problem and the calculus of variations }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 35 }, Series = { Math.\ Notes }, Year = { 1988 } } @Article{ Str89, Author = { M. Struwe }, Title = { {E}xistence and partial regularity results for the heat flow for harmonic maps }, Journal = { Math.\ Z. }, Volume = { 201 }, Pages = { 83-103 }, Year = { 1989 } } @Incollection{ Str90, Author = { M. Struwe }, Title = { {G}lobal existence and partial regularity results for the evolution of harmonic maps }, Booktitle = { {V}ariational {M}ethods }, Editor = { H. Berestycki and J.-M. Coron and I. Ekeland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 4 }, Pages = { 359-369 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1990 } } @Incollection{ Str90A, Author = { M. Struwe }, Title = { {V}ariational {M}ethods }, Booktitle = { {A}pplications to nonlinear partial differential equations and {H}amiltonian systems }, Publisher = { Springer }, Year = { 1990 } } @Article{ Str91, Author = { M. Struwe }, Title = { {T}he evolution of harmonic mappings with free boundaries }, Journal = { Manuscripta Math. }, Volume = { 70 }, Pages = { 373-384 }, Year = { 1991 } } @Incollection{ Str91A, Author = { M. Struwe }, Title = { {T}he evolution of harmonic maps }, Booktitle = { {P}roc. {I}{C}{M} {K}yoto 1990, {I}{I} }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Pages = { 1197-1203 }, Year = { 1991 } } @Unpublished{ Str91B, Author = { M. Struwe }, Title = { {M}inimal surfaces of higher genus and general critical type }, Note = { Nankai Inst. }, Year = { 1991 } } @Incollection{ Str92, Author = { M. Struwe }, Title = { {O}n the evolution of harmonic maps, existence, partial regularity and singularities }, Booktitle = { {N}onlinear diffusion equations and their equilibrium states, 3 }, Editor = { N.G. Lloyd and W.M. Ni and L.A. Peletier and J. Serrin }, Publisher = { Birkh{\"a}user }, Address = { Boston }, Volume = { 7 }, Pages = { 485-491 }, Series = { Progr.\ Nonlinear Differential Equations Appl. }, Year = { 1992 } } @Article{ Str94, Author = { M. Struwe }, Title = { {D}as {P}lateausche {P}roblem }, Journal = { Jahresber.\ Deutsch.\ Math.-Verein. }, Volume = { 96 }, Pages = { 101-116 }, Year = { 1994 } } @Incollection{ Str96, Author = { M. Struwe }, Title = { {G}eometric evolution problems }, Booktitle = { {N}onlinear partial differential equations in differential geometry ({P}ark {C}ity, {U}{T}, 1992) }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 2 }, Pages = { 257-339 }, Series = { IAS/Park City Math.\ Ser. }, Year = { 1996 } } @Article{ Str94A, Author = { P. Strzelecki }, Title = { {R}egularity of {$p$}-harmonic maps from the {$p$}-dimensional ball into a sphere }, Journal = { Manuscripta Math. }, Volume = { 82 }, Pages = { 407-415 }, Year = { 1994 } } @Article{ Str96A, Author = { P. Strzelecki }, Title = { {S}tationary {$p$}-harmonic maps into spheres }, Journal = { Banach Center Publ. }, Volume = { 33 }, Pages = { 383--393 }, Year = { 1996 } } @Article{ Str85C, Author = { G. Str{\"o}hmer }, Title = { {A}bout the {M}orse theory for certain variational problems }, Journal = { Math.\ Ann. }, Volume = { 270 }, Pages = { 275-284 }, Year = { 1985 } } @Incollection{ Str92A, Author = { G. Str{\"o}hmer }, Title = { {T}he parametric {P}lateau problem and related topics }, Booktitle = { {T}he {P}roblem of {P}lateau }, Editor = { T.M. Rassias }, Publisher = { World Scientific }, Address = { River Edge, NJ }, Pages = { 258-284 }, Year = { 1992 } } @Unpublished{ StrF, Author = { W. Str{\"u}bing }, Title = { {I}soparametric submanifolds }, Note = { preprint } } @Article{ Stu83, Author = { S. Stuart }, Title = { {S}ome aspects of the {${C}{P}^{{N}-1}$} model }, Journal = { Phys.\ Rev.\ D }, Volume = { 28 }, Pages = { 2628-2636 }, Year = { 1983 } } @Article{ Stu81, Author = { S.M. Stumbles }, Title = { {H}ypersurfaces of constant mean extrinsic curvature }, Journal = { Ann.\ Physics }, Volume = { 133 }, Pages = { 28-56 }, Year = { 1981 } } @Article{ Sul79, Author = { D. Sullivan }, Title = { {A} homological characterization of foliations consisting of minimal surfaces }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 54 }, Pages = { 218-223 }, Year = { 1979 } } @Article{ Sul83, Author = { D. Sullivan }, Title = { {T}he {D}irichlet problem at infinity for a negatively curved manifold }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 723-732 }, Year = { 1983 } } @Incollection{ Sum93, Author = { M. Sumi }, Title = { {$p$}-harmonic maps and symmetric spaces }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 465-467 }, Year = { 1993 } } @Article{ Sun92, Author = { H.A. Sun }, Title = { {C}ompositions of {$2$}-harmonic maps }, Journal = { J. Math.\ Res.\ Exposition }, Volume = { 12 }, Pages = { 535-538 }, Note = { (Chinese) }, Year = { 1992 } } @Article{ Sun92A, Author = { H.A. Sun }, Title = { {A} theorem on {$2$}-harmonic mappings }, Journal = { J. Math.\ (Wuhan) }, Volume = { 12 }, Pages = { 103-106 }, Note = { (Chinese, English summary) }, Year = { 1992 } } @Article{ Sun93, Author = { H.A. Sun }, Title = { {$2$}-harmonic isometric immersions with parallel mean curvature vector }, Journal = { J. Math.\ (Wuhan) }, Volume = { 13 }, Pages = { 141--146 }, Note = { (Chinese with English summary) }, Year = { 1993 } } @Article{ Sun94, Author = { H.A. Sun }, Title = { {$2$}-harmonic isometric immersions in a sphere with parallel mean curvature vector }, Journal = { Pure Appl.\ Math. }, Volume = { 10 }, Pages = { 114-118 }, Note = { (Chinese with English summary) }, Year = { 1994 } } @Article{ Sun92B, Author = { H.F. Sun }, Title = { {T}otally real minimal submanifolds in complex projective spaces }, Journal = { J. Northeast.\ Univ.\ Tech. }, Volume = { 13 }, Pages = { 313-317 }, Year = { 1992 } } @Misc{ Sun, Author = { T. Sunada }, Title = { {F}undamental group of a family of certain holomorphic mappings } } @Article{ Sun79, Author = { T. Sunada }, Title = { {R}igidity of certain harmonic mappings }, Journal = { Invent.\ Math. }, Volume = { 51 }, Pages = { 297-307 }, Year = { 1979 } } @Article{ SunTamWan96, Author = { C.J. Sung and L.F. Tam and J. Wang }, Title = { {B}ounded harmonic maps on a class of manifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 124 }, Pages = { 2241-2248 }, Year = { 1996 } } @Article{ Suy70, Author = { Y. Suyama }, Title = { {O}n a problem proposed by {E}ells--{S}ampson }, Journal = { Mem.\ Fac.\ Sci.\ Kyushu Univ.\ Ser.\ A }, Volume = { 24 }, Pages = { 305-315 }, Year = { 1970 } } @Unpublished{ Suz, Author = { O. Suzuki }, Title = { {P}seudoconvexity and holomorphic bisectional curvature on {K}\"ahler manifolds }, Note = { preprint } } @Incollection{ Suz80, Author = { O. Suzuki }, Title = { {T}heorems on holomorphic bisectional curvature and pseudoconvexity on {K}\"ahler manifolds }, Booktitle = { {A}nalytic functions }, Editor = { J. Lawrynowicz }, Publisher = { Springer }, Address = { Berlin }, Volume = { 798 }, Pages = { 412-428 }, Series = { Lecture Notes in Math. }, Year = { 1980 } } @Incollection{ Sym85, Author = { A. Sym }, Title = { {S}oliton surfaces and their applications }, Booktitle = { {G}eometric aspects of the {E}instein equations and integrable systems }, Editor = { R. Martini }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York, Tokyo }, Volume = { 239 }, Pages = { 154-231 }, Series = { Lecture Notes in Phys. }, Year = { 1985 } } @Article{ Sza90, Author = { Z. Szab{\'o} }, Title = { {T}he {L}ichnerowicz conjecture on harmonic manifolds }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 1-28 }, Year = { 1990 } } @Incollection{ Sza93, Author = { Z. Szab{\'o} }, Title = { {S}pectral theory for operator families on {R}iemannian manifolds }, Booktitle = { {D}ifferential {G}eometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 54 (Part 3) }, Pages = { 615-665 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ Szu78, Author = { A. Szulkin }, Title = { {A}n example concerning the topological character of the zero-set of a harmonic function }, Journal = { Math.\ Scand. }, Volume = { 43 }, Pages = { 60-62 }, Year = { 1978 } } @Article{ Sol, Author = { M. S{\"o}llner }, Title = { {P}lateau's problem for surfaces of constant mean curvature... }, Journal = { Manuscripta Math. } } @Article{ San82, Author = { N. S{\'a}nchez }, Title = { {C}onnection between the non-linear sigma-model and the {E}instein equations of general relativity }, Journal = { Phys.\ Rev.\ D }, Volume = { 26 }, Pages = { 2589-2597 }, Year = { 1982 } } @Article{ San83B, Author = { N. S{\'a}nchez }, Title = { {N}ew solutions of {E}instein equations from analytic mappings }, Journal = { Phys.\ Lett.\ A }, Volume = { 94 }, Pages = { 125 }, Year = { 1983 } } @Article{ San84, Author = { N. S{\'a}nchez }, Title = { {C}onnection between the self-dual {Y}ang--{M}ills and {E}instein equations }, Journal = { Phys.\ Lett.\ B }, Volume = { 144 }, Pages = { 217 }, Year = { 1984 } } @Incollection{ San85A, Author = { N. S{\'a}nchez }, Title = { {E}instein equations, non-linear {$\sigma$}-models and self-dual {Y}ang--{M}ills theory }, Booktitle = { {C}lausthal {P}roceedings }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Series = { Lecture Notes in Math. }, Year = { 1985 } } @Incollection{ San85B, Author = { N. S{\'a}nchez }, Title = { {E}xact solutions in gauge theory, general relativity and their supersymmetric extensions }, Booktitle = { {G}eometric aspects of the {E}instein equations and integrable systems }, Editor = { R. Martini }, Volume = { 239 }, Pages = { 1-77 }, Series = { Lecture Notes in Phys. }, Year = { 1985 } } @Unpublished{ San86, Author = { N. S{\'a}nchez }, Title = { {H}armonic maps in general relativity and quantum field theory }, Note = { Preprint, CERN }, Year = { 1986 } } @Incollection{ s81, Author = { S. Ianu{\c s} }, Title = { {S}ome submanifolds of the tangent bundle }, Booktitle = { {T}he {P}roceedings of the {N}ational {S}eminar on {F}insler {S}paces ({B}ra{\c s}ov, 1980), {U}niv. {T}imi{\c s}oara }, Publisher = { Univ.\ Timi{\c s}oara }, Address = { Timi{\c s}oara }, Pages = { 69-75 }, Year = { 1981 } } @Misc{ sOrnVul, Author = { S. Ianu{\c s} and L. Ornea and V. Vuletscu }, Title = { {H}olomorphic and harmonic maps of locally conformal {K}{\"a}hler manifolds } } @Article{ sca81, Author = { R. Ro{\c s}ca }, Title = { {O}n the codimension {$n$} minimal surfaces carrying a covariant decomposable tangential vector field in a {R}iemannian or pseudo-{R}iemannian space form }, Journal = { Libertas Math. }, Volume = { 1 }, Pages = { 141-149 }, Year = { 1981 } } @Article{ ska87, Author = { O. Mu{\v s}karov }, Title = { {S}tructures presques hermitiennes sur des espaces twistoriels et leurs types }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 305 }, Pages = { 307-309 }, Year = { 1987 } } @Article{ ska89, Author = { O. Mu{\v s}karov }, Title = { {A}lmost {H}ermitian structures on twistor spaces and their types }, Journal = { Atti Sem.\ Mat.\ Fis.\ Univ.\ Modena }, Volume = { 37 }, Pages = { 285-297 }, Year = { 1989 } } @Article{ Sve76, Author = { A. {\u S}vec }, Title = { {H}armonic mappings of surfaces }, Journal = { \v Casopis P\v est.\ Mat. }, Volume = { 101 }, Pages = { 283-292 }, Year = { 1976 } } @Article{ Sve88, Author = { A. {\u S}vec }, Title = { {O}n {V}eronese surfaces }, Journal = { Czechoslovak Math.\ J. }, Volume = { 38 }, Year = { 1988 } } @Unpublished{ Tab82, Author = { B.L. Tabak }, Title = { {H}armonic maps and measured foliations }, Note = { Brown Univ. Ph.D Thesis }, Year = { 1982 } } @Article{ Tab85, Author = { B.L. Tabak }, Title = { {A} geometric characterisation of harmonic diffeomorphisms between surfaces }, Journal = { Math.\ Ann. }, Volume = { 270 }, Pages = { 147-157 }, Year = { 1985 } } @Article{ Tac83, Author = { A. Tachikawa }, Title = { {O}n interior regularity and {L}iouville's theorem for harmonic mappings }, Journal = { Manuscripta Math. }, Volume = { 42 }, Pages = { 11-40 }, Year = { 1983 } } @Article{ Tac85, Author = { A. Tachikawa }, Title = { {R}otationally symmetric harmonic maps from a ball into a warped product manifold }, Journal = { Manuscripta Math. }, Volume = { 53 }, Pages = { 235-254 }, Year = { 1985 } } @Article{ Tac87, Author = { A. Tachikawa }, Title = { {A} regularity theorem for harmonic mappings }, Journal = { J. Reine Angew.\ Math. }, Volume = { 377 }, Pages = { 1-11 }, Year = { 1987 } } @Article{ Tac88, Author = { A. Tachikawa }, Title = { {A} non-existence result for harmonic mappings from {${\bf {R}}^n$} to {${H}^n$} }, Journal = { Tokyo J. Math. }, Volume = { 11 }, Pages = { 311-316 }, Year = { 1988 } } @Article{ Tac90, Author = { A. Tachikawa }, Title = { {H}armonic mappings from {${\bf {R}}^n$} into a {H}adamard manifold }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 42 }, Pages = { 147-153 }, Year = { 1990 } } @Article{ Tac92, Author = { A. Tachikawa }, Title = { {H}armonic maps from a {R}iemannian manifold with a pole into an {H}adamard manifold with negative sectional curvatures }, Journal = { Manuscripta Math. }, Volume = { 74 }, Pages = { 69-81 }, Year = { 1992 } } @Article{ Tak85, Author = { H. Takagi }, Title = { {A} condition for isoparametric hypersurfaces of {${S}^n$} to be homogeneous }, Journal = { T\^ohoku Math.\ J. }, Volume = { 37 }, Pages = { 241-250 }, Year = { 1985 } } @Article{ Tak76, Author = { R. Takagi }, Title = { {A} class of hypersurfaces with constant principal curvatures in a sphere }, Journal = { J. Differential Geom. }, Volume = { 11 }, Pages = { 225-233 }, Year = { 1976 } } @Incollection{ TakTak72, Author = { R. Takagi and T. Takahashi }, Title = { {O}n the principal curvatures of homogeneous hypersurfaces in a sphere }, Booktitle = { {D}ifferential {G}eometry in honour of {K}. {Y}ano, {T}okyo }, Pages = { 469-481 }, Year = { 1972 } } @Article{ TakYor84, Author = { R. Takagi and S. Yorozu }, Title = { {M}inimal foliations on {L}ie groups }, Journal = { T\^ohoku Math.\ J. }, Volume = { 36 }, Pages = { 541-554 }, Year = { 1984 } } @Article{ Tak66, Author = { T. Takahashi }, Title = { {M}inimal immersions of {R}iemannian manifolds }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 18 }, Pages = { 380-385 }, Year = { 1966 } } @Article{ Tak85A, Author = { S. Takakuwa }, Title = { {O}n removable singularities of certain harmonic maps }, Journal = { Proc.\ Japan Acad.\ Ser.\ A Math.\ Sci. }, Volume = { 61 }, Pages = { 103-106 }, Year = { 1985 } } @Article{ Tak85B, Author = { S. Takakuwa }, Title = { {O}n removable singularities of stationary harmonic maps }, Journal = { J. Fac.\ Sci.\ Univ.\ Tokyo Sect.\ IA Math. }, Volume = { 32 }, Pages = { 373-395 }, Year = { 1985 } } @Article{ Tak86, Author = { K. Takegoshi }, Title = { {A} non-existence theorem for pluriharmonic maps of finite energy }, Journal = { Math.\ Z. }, Volume = { 192 }, Pages = { 21-27 }, Year = { 1986 } } @Article{ Tak90, Author = { K. Takegoshi }, Title = { {E}nergy estimates and {L}iouville theorems for harmonic maps }, Journal = { Ann.\ Sci.\ \'Ecole Norm.\ Sup. }, Volume = { 23 }, Pages = { 563-592 }, Year = { 1990 } } @Incollection{ Tak77, Author = { F. Takens }, Title = { {S}ymmetries, conservation laws and variational principles }, Booktitle = { {G}eometry and {T}opology }, Editor = { J. Palis and M.P. do~Carmo }, Publisher = { Springer }, Address = { Berlin }, Volume = { 597 }, Pages = { 581-603 }, Series = { Lecture Notes in Math. }, Year = { 1977 } } @Article{ Tak79, Author = { F. Takens }, Title = { {A} global version of the inverse problem of the calculus of variations }, Journal = { J. Differential Geom. }, Volume = { 14 }, Pages = { 543-563 }, Year = { 1979 } } @Article{ Tak82, Author = { H. Takeuchi }, Title = { {A} stable harmonic map of a manifold with boundary }, Journal = { Comment.\ Math.\ Univ.\ St.\ Paul. }, Volume = { 31 }, Pages = { 223-230 }, Year = { 1982 } } @Article{ Tak91, Author = { H. Takeuchi }, Title = { {S}tability and {L}iouville theorems of {$p$}-harmonic maps }, Journal = { Japan J. Math.\ (N.S.) }, Volume = { 17 }, Pages = { 317-332 }, Year = { 1991 } } @Article{ Tak94, Author = { H. Takeuchi }, Title = { {S}ome conformal properties of {$p$}-harmonic maps and regularity for sphere-valued {$p$}-harmonic maps }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 46 }, Pages = { 217-234 }, Year = { 1994 } } @Article{ Tak84, Author = { M. Takeuchi }, Title = { {S}tability of certain minimal submanifolds of compact {H}ermitian symmetric spaces }, Journal = { T\^ohoku Math.\ J. }, Volume = { 36 }, Pages = { 293-314 }, Year = { 1984 } } @Unpublished{ Tal81, Author = { G. Talenti }, Title = { {A} note on the {G}auss curvature of harmonic and minimal surfaces }, Note = { Univ. Firenze, preprint }, Year = { 1980/81 } } @Article{ Tam92, Author = { L.F. Tam }, Title = { {H}armonic functions on connected sums of manifolds }, Journal = { Math.\ Z. }, Volume = { 211 }, Pages = { 315-322 }, Year = { 1992 } } @Article{ Tam95, Author = { L.F. Tam }, Title = { {L}iouville property for harmonic maps on a class of manifolds }, Journal = { Math.\ Res.\ Lett. }, Volume = { 2 }, Pages = { 719-735 }, Year = { 1995 } } @Article{ TamWan, Author = { L.F. Tam and T.Y.H. Wan }, Title = { {H}armonic diffeomorphisms into {C}artan-{H}adamard surfaces with prescribed {H}opf differentials }, Journal = { Comm.\ Anal.\ Geom. } } @Misc{ TamWanA, Author = { L.F. Tam and T.Y.H. Wan }, Title = { {Q}uasi-conformal harmonic diffeomorphisms and the universal {T}eichm\"uller space } } @Article{ Tan95, Author = { M.S. Tanaka }, Title = { {S}tability of minimal submanifolds in symmetric spaces }, Journal = { Tsukuba J. Math. }, Volume = { 19 }, Pages = { 27-56 }, Year = { 1995 } } @Article{ Tan87, Author = { S. Tanno }, Title = { {I}nstability of spheres with deformed {R}iemannian metrics }, Journal = { Kodai Math.\ J. }, Volume = { 10 }, Pages = { 250-257 }, Year = { 1987 } } @Article{ Tan93, Author = { S. Tanno }, Title = { {T}he identity map as a harmonic map of a {$(4r+3)$}-sphere with deformed metrics }, Journal = { Kodai Math.\ J. }, Volume = { 16 }, Pages = { 171-180 }, Year = { 1993 } } @Article{ Tan77, Author = { G.E. Tanyi }, Title = { {S}ur les points critiques de la fonctionnelle d'\'energie \'elastique classique }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 285 }, Pages = { 867-869 }, Year = { 1977 } } @Article{ Tas85, Author = { H. Tasaki }, Title = { {C}ertain minimal or homologically volume minimizing submanifolds in compact symmetric spaces }, Journal = { Tsukuba J. Math. }, Volume = { 9 }, Pages = { 117-131 }, Year = { 1985 } } @Article{ Tas86, Author = { H. Tasaki }, Title = { {Q}uaternionic submanifolds in quaternionic spaces }, Journal = { T\^ohoku Math.\ J. }, Volume = { 38 }, Pages = { 513-533 }, Year = { 1986 } } @Article{ Tas88, Author = { H. Tasaki }, Title = { {C}alibrated geometries in quaternionic {G}rassmannians }, Journal = { Osaka J. Math. }, Volume = { 25 }, Pages = { 591-598 }, Year = { 1988 } } @Incollection{ Tem81, Author = { R. Temam }, Title = { {S}urfaces minimales et plasticit{\'e} }, Booktitle = { {N}onlinear partial differential equations and their applications, {C}oll. de {F}rance {S}em. {V}ol. {I} }, Editor = { H. Brezis and J.L. Lions }, Publisher = { Pitman }, Address = { Boston, Mass. }, Volume = { 53 }, Pages = { 378-388 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1981 } } @Article{ Ter78, Author = { C.L. Terng }, Title = { {N}atural vector bundles and differential operators }, Journal = { Amer.\ J. Math. }, Volume = { 100 }, Pages = { 775-828 }, Year = { 1978 } } @Article{ Ter85, Author = { C.L. Terng }, Title = { {I}soparametric submanifolds and their {C}oxeter groups }, Journal = { J. Differential Geom. }, Volume = { 21 }, Pages = { 79-107 }, Year = { 1985 } } @Article{ Ter97, Author = { C.L. Terng }, Title = { {S}oliton equations and differential geometry }, Journal = { J. Differential Geom. }, Volume = { 45 }, Pages = { 407-445 }, Year = { 1997 } } @Article{ Tha96, Author = { A. Thalmaier }, Title = { {B}rownian motion and the formation of singularities in the heat flow for harmonic maps }, Journal = { Probab.\ Theory Related Fields }, Volume = { 105 }, Pages = { 335--367 }, Year = { 1996 } } @Article{ Tha88, Author = { C. Thas }, Title = { {A} property of the {V}eronese surface }, Journal = { J. Geom. }, Volume = { 32 }, Pages = { 157-168 }, Year = { 1988 } } @Article{ Thi81, Author = { D.C. Thi }, Title = { {M}ultivarifolds and classical multidimensional {P}lateau problems }, Journal = { Math.\ USSR-Izv. }, Volume = { 17 }, Pages = { 271-298 }, Year = { 1981 } } @Article{ Thi85, Author = { U. Thiel }, Title = { {T}he index theorem for {$k$}-fold connected minimal surfaces }, Journal = { Math.\ Ann. }, Volume = { 270 }, Pages = { 489-501 }, Year = { 1985 } } @Article{ Thi85A, Author = { U. Thiel }, Title = { {O}n the stratification of branched minimal surfaces }, Journal = { Analysis }, Volume = { 5 }, Pages = { 251-274 }, Year = { 1985 } } @Book{ Tho34, Author = { T.Y. Thomas }, Title = { {D}ifferential invariants of generalized spaces }, Publisher = { Camb.\ Univ.\ Press }, Year = { 1934 } } @Article{ Thu76, Author = { W.P. Thurston }, Title = { {S}ome simple examples of symplectic manifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 55 }, Pages = { 467-468 }, Year = { 1976 } } @Incollection{ Tod95, Author = { K.P. Tod }, Title = { {M}onopoles, harmonic morphisms and spinor fields }, Booktitle = { {F}urther {A}dvances in {T}wistor {T}heory: {V}ol. {I}{I}: {I}ntegrable systems, conformal geometry and gravitation }, Editor = { L.J. Mason and L.P. Hughston and P.Z. Kobak }, Publisher = { Longman }, Address = { Harlow }, Volume = { 232 }, Pages = { 45-46 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1995 } } @Incollection{ Tod95A, Author = { K.P. Tod }, Title = { {M}ore on harmonic morphisms }, Booktitle = { {F}urther {A}dvances in {T}wistor {T}heory: {V}ol. {I}{I}: {I}ntegrable systems, conformal geometry and gravitation }, Editor = { L.J. Mason and L.P. Hughston and P.Z. Kobak }, Publisher = { Longman }, Address = { Harlow }, Volume = { 232 }, Pages = { 47-48 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1995 } } @Article{ Tol78, Author = { D. Toledo }, Title = { {H}armonic maps from surfaces to certain {K}\"ahler manifolds }, Journal = { Math.\ Scand. }, Volume = { 45 }, Pages = { 13-26 }, Year = { 1978 } } @Article{ Tol88, Author = { D. Toledo }, Title = { {B}ounded harmonic functions on coverings }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 104 }, Pages = { 1218-1219 }, Year = { 1988 } } @Article{ Tol89, Author = { D. Toledo }, Title = { {R}epresentations of surface groups in complex hyperbolic space }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 125-133 }, Year = { 1989 } } @Article{ Tol90, Author = { D. Toledo }, Title = { {E}xamples of fundamental groups of compact {K}{\"a}hler manifolds }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 22 }, Pages = { 339-343 }, Year = { 1990 } } @Article{ Tol93, Author = { D. Toledo }, Title = { {P}rojective varieties with non-residually finite fundamental group }, Journal = { Inst.\ Hautes \'Etudes Sci.\ Publ.\ Math. }, Volume = { 77 }, Pages = { 103-119 }, Year = { 1993 } } @Article{ Tol83, Author = { P. Tolksdorf }, Title = { {E}verywhere regularity for some quasi-linear systems with a lack of ellipticity }, Journal = { Ann.\ Mat.\ Pura Appl.\ (4) }, Volume = { 134 }, Pages = { 241-266 }, Year = { 1983 } } @Unpublished{ Tol83A, Author = { P. Tolksdorf }, Title = { {A} strong maximum principle and regularity for harmonic mappings }, Note = { SFB 72 Bonn Preprint }, Year = { 1983 } } @Article{ Tol84, Author = { P. Tolksdorf }, Title = { {A} parametric variational principle for minimal surface of varying topological type }, Journal = { J. Reine Angew.\ Math. }, Volume = { 354 }, Pages = { 16-49 }, Year = { 1984 } } @Article{ Tol84A, Author = { P. Tolksdorf }, Title = { {R}egularity for a more general class of quasi-linear elliptic equations }, Journal = { J. Differential Equations }, Volume = { 51 }, Pages = { 126-150 }, Year = { 1984 } } @Article{ Tol84B, Author = { P. Tolksdorf }, Title = { {A} strong maximum principle and regularity for harmonic mappings }, Journal = { Rend.\ Mat. }, Volume = { 4 }, Pages = { 561-573 }, Year = { 1984 } } @Article{ Tol85, Author = { P. Tolksdorf }, Title = { {O}n minimal surfaces with free boundaries in given homotopy classes }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 2 }, Pages = { 157-165 }, Year = { 1985 } } @Misc{ Tom, Author = { F. Tomi }, Title = { {A} finiteness result in the free boundary problem for minimal surfaces } } @Article{ Tom69, Author = { F. Tomi }, Title = { {E}in einfacher {B}eweis eines {R}egularit\"atssatzes f\"ur schwache {L}\"osungen gewisser elliptischer {S}ysteme }, Journal = { Math.\ Z. }, Volume = { 112 }, Pages = { 214-218 }, Year = { 1969 } } @Article{ Tom75, Author = { F. Tomi }, Title = { {A} perturbation theorem for surfaces of constant mean curvature }, Journal = { Math.\ Z. }, Volume = { 141 }, Pages = { 253-264 }, Year = { 1975 } } @Misc{ TomTro, Author = { F. Tomi and A.J. Tromba }, Title = { {O}n {P}lateau's problem for minimal surfaces of prescribed topological type } } @Article{ TomTro85, Author = { F. Tomi and A.J. Tromba }, Title = { {O}n {P}lateau's problem for minimal surfaces of higher genus in {${\bf {R}}^3$} }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 13 }, Pages = { 169-171 }, Year = { 1985 } } @Book{ TomTro88, Author = { F. Tomi and A.J. Tromba }, Title = { {E}xistence theorems for minimal surfaces of non-zero genus spanning a contour }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 382 }, Series = { Mem.\ Amer.\ Math.\ Soc. }, Year = { 1988 } } @Misc{ TomYe, Author = { F. Tomi and R. Ye }, Title = { {T}he exterior {P}lateau problem } } @Article{ Tom84, Author = { P. Tomter }, Title = { {T}he spherical {B}ernstein problem in even dimensions }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 11 }, Pages = { 183-185 }, Year = { 1984 } } @Article{ Tom87, Author = { P. Tomter }, Title = { {T}he spherical {B}ernstein problem in even dimensions and related problems }, Journal = { Acta Math. }, Volume = { 158 }, Pages = { 189-212 }, Year = { 1987 } } @Article{ Tom88, Author = { P. Tomter }, Title = { {E}xistence and uniqueness for a class of {C}auchy problems with characteristic initial manifolds }, Journal = { J. Differential Equations }, Volume = { 71 }, Pages = { 1-9 }, Year = { 1988 } } @Incollection{ Tom93, Author = { P. Tomter }, Title = { {C}onstant mean curvature surfaces in the {H}eisenberg group }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 485-495 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Incollection{ Tom93A, Author = { P. Tomter }, Title = { {O}n dynamical systems and the minimal surface equation }, Booktitle = { {P}roc. {S}malefest }, Publisher = { Springer }, Pages = { 259-269 }, Year = { 1993 } } @Incollection{ Ton88, Author = { P. Tondeur }, Title = { {T}he mean curvature of {R}iemannian foliations }, Booktitle = { {F}euilletages riemanniens, quantification g{\'e}om{\'e}trique et m{\'e}canique }, Publisher = { Hermann }, Address = { Paris }, Pages = { 41-52 }, Series = { Travaux en Cours }, Year = { 1988 } } @Article{ TonTot87, Author = { P. Tondeur and G. Toth }, Title = { {O}n transversal infinitesimal automorphisms for harmonic foliations }, Journal = { Geom.\ Dedicata }, Volume = { 24 }, Pages = { 229-236 }, Year = { 1987 } } @Article{ TonVan, Author = { P. Tondeur and L. Vanhecke }, Title = { {H}armonicity of a foliation and of an associated map }, Journal = { Bull.\ Austral.\ Math.\ Soc. }, Note = { (to appear) } } @Misc{ Top, Author = { P. Topping }, Title = { {A}n example of a nontrivial bubble tree in the harmonic heat flow } } @Misc{ TopA, Author = { P. Topping }, Title = { {U}niqueness and non-uniqueness of limits of the harmonic heat flow } } @Unpublished{ Top93, Author = { P. Topping }, Title = { {T}he heat equation for maps between manifolds }, Note = { Warwick M. Sc. Thesis }, Year = { 1993 } } @Misc{ TorWan, Author = { T. Toro and C. Wang }, Title = { {C}ompactness properties of weakly p-harmonic maps into homogeneous spaces } } @Article{ Tot, Author = { G. Toth }, Title = { {E}igenmaps and the space of minimal immersions between spheres }, Journal = { Indiana Univ.\ Math.\ J. } } @Misc{ TotA, Author = { G. Toth }, Title = { {M}oduli spaces of harmonic maps between complex projective spaces } } @Article{ Tot79, Author = { G. Toth }, Title = { {E}xtension of a theorem of {A}. {L}ichnerowicz }, Journal = { Proc.\ Fac.\ Sci.\ Tokai Univ. }, Volume = { 15 }, Pages = { 29-32 }, Year = { 1979 } } @Article{ Tot81, Author = { G. Toth }, Title = { {O}n homotopy classes of mappings into flat {R}iemannian manifolds }, Journal = { Publ.\ Math.\ Debrecen }, Volume = { 28 }, Pages = { 231-245 }, Year = { 1981 } } @Article{ Tot81A, Author = { G. Toth }, Title = { {O}n variations of harmonic maps into spaces of constant curvature }, Journal = { Ann.\ di Mat. }, Volume = { 128 }, Pages = { 389-399 }, Year = { 1981 } } @Article{ Tot82, Author = { G. Toth }, Title = { {H}armonic submersion onto nonnegatively curved manifolds }, Journal = { Acta Math.\ Hungar. }, Volume = { 39 }, Pages = { 49-53 }, Year = { 1982 } } @Article{ Tot82A, Author = { G. Toth }, Title = { {O}n harmonic maps into locally symmetric {R}iemannian manifolds }, Journal = { Sympos.\ Math. }, Volume = { 26 }, Pages = { 69-94 }, Year = { 1982 } } @Article{ Tot82B, Author = { G. Toth }, Title = { {O}n rigidity of harmonic mappings into spheres }, Journal = { J. London Math.\ Soc. }, Volume = { 26 }, Pages = { 475-486 }, Year = { 1982 } } @Article{ Tot83, Author = { G. Toth }, Title = { {C}onstruction des applications harmoniques non rigides d'un tore dans la sph\ `ere }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 1 }, Pages = { 105-118 }, Year = { 1983 } } @Article{ Tot83A, Author = { G. Toth }, Title = { {O}ne-parameter families of harmonic maps into spaces of constant curvature }, Journal = { Studia Sci.\ Math.\ Hungar. }, Volume = { 18 }, Pages = { 183-193 }, Year = { 1983 } } @Incollection{ Tot84, Author = { G. Toth }, Title = { {F}lexible harmonic maps into spheres }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 156-167 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Book{ Tot84A, Author = { G. Toth }, Title = { {H}armonic and minimal maps with applications in geometry and physics }, Publisher = { E. Horwood }, Address = { Chichester }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Article{ Tot84B, Author = { G. Toth }, Title = { {O}n naturally reductive homogeneous spaces harmonically embedded into spheres }, Journal = { J. London Math.\ Soc. }, Volume = { 29 }, Pages = { 175-180 }, Year = { 1984 } } @Article{ Tot84C, Author = { G. Toth }, Title = { {T}oroidal group actions on compact {R}iemannian manifolds and their relations to the fibring problem }, Journal = { Diff.\ Geom.\ Banach Centre Publ.\ Warsaw }, Volume = { 12 }, Pages = { 233-240 }, Year = { 1984 } } @Article{ Tot85, Author = { G. Toth }, Title = { {O}n non-rigidity of harmonic maps into spheres }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 94 }, Pages = { 711-714 }, Year = { 1985 } } @Article{ Tot87, Author = { G. Toth }, Title = { {C}lassification of quadratic harmonic maps of {${S}^3$} into spheres }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 36 }, Pages = { 231-239 }, Year = { 1987 } } @Article{ Tot87A, Author = { G. Toth }, Title = { {O}n classification of orthogonal multiplications \`a la do {C}armo--{W}allach }, Journal = { Geom.\ Dedicata }, Volume = { 22 }, Pages = { 251-254 }, Year = { 1987 } } @Incollection{ Tot88, Author = { G. Toth }, Title = { {M}oduli spaces of harmonic maps between spheres and complex projective spaces }, Booktitle = { {G}eo. and {T}op. }, Publisher = { World Sci. }, Year = { 1988 } } @Article{ Tot88A, Author = { G. Toth }, Title = { {O}n classification of quadratic harmonic maps of {${S}^3$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 102 }, Pages = { 174-176 }, Year = { 1988 } } @Book{ Tot90, Author = { G. Toth }, Title = { {H}armonic maps and minimal immersions through representation theory }, Publisher = { Academic Press }, Series = { Perspect.\ Math. }, Year = { 1990 } } @Article{ Tot90A, Author = { G. Toth }, Title = { {M}oduli spaces of polynomial minimal immersions between complex projective spaces }, Journal = { Michigan Math.\ J. }, Volume = { 37 }, Pages = { 385-396 }, Year = { 1990 } } @Article{ Tot92, Author = { G. Toth }, Title = { {M}appings of moduli spaces for harmonic eigenmaps and minimal immersions between spheres }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 44 }, Pages = { 179-198 }, Year = { 1992 } } @Incollection{ Tot92A, Author = { G. Toth }, Title = { {O}n the number of rigid minimal immersions between spheres }, Booktitle = { {T}he {P}roblem of {P}lateau }, Publisher = { World Sci. }, Address = { Singapore }, Year = { 1992 } } @Article{ Tot93, Author = { G. Toth }, Title = { {O}perators on {E}igenmaps between {S}pheres }, Journal = { Compositio Math. }, Volume = { 88 }, Pages = { 317-332 }, Year = { 1993 } } @Article{ Tot93A, Author = { G. Toth }, Title = { {R}igidity of minimal submanifolds in spheres in terms of higher fundamental forms }, Journal = { Michigan Math.\ J. }, Volume = { 40 }, Pages = { 493-505 }, Year = { 1993 } } @Article{ Tot95, Author = { G. Toth }, Title = { {O}n the structure of the moduli space of harmonic eigenmaps }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 47 }, Pages = { 503-522 }, Year = { 1995 } } @Article{ Tot95A, Author = { G. Toth }, Title = { {Q}uadratic eigenmaps between spheres }, Journal = { Geom.\ Dedicata }, Volume = { 56 }, Pages = { 35-52 }, Year = { 1995 } } @Article{ Tou, Author = { E. Toubiana }, Title = { {O}n the uniqueness of the helicoid }, Journal = { Ann.\ Inst.\ Fourier (Grenoble) } } @Article{ Tou93, Author = { E. Toubiana }, Title = { {S}urfaces minimales non orientables de genre quelconque }, Journal = { Bull.\ Soc.\ Math.\ France }, Volume = { 121 }, Pages = { 183-195 }, Year = { 1993 } } @Unpublished{ TraVal94, Author = { S. Trapani and G. Valli }, Title = { {O}ne-harmonic maps on {R}iemann surfaces }, Note = { Preprint }, Year = { 1994 } } @Misc{ Tre, Author = { A. Treibergs }, Title = { {L}ecture on the {E}ells--{S}ampson theorem on parabolic deformation of maps to harmonic maps } } @Misc{ TreA, Author = { A. Treibergs }, Title = { {M}ultiple harmonic diffeomorphisms from the complex plane to ideal polygons of the hyperbolic disk } } @Article{ Tre82, Author = { A. Treibergs }, Title = { {E}ntire spacelike hypersurfaces of constant mean curvature in {M}inkowski space }, Journal = { Invent.\ Math. }, Volume = { 66 }, Pages = { 39-56 }, Year = { 1982 } } @Article{ Tre85, Author = { A. Treibergs }, Title = { {E}xistence and convexity for hyperspheres of prescribed mean curvature }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 2 }, Pages = { 225-241 }, Year = { 1985 } } @Article{ Tre90, Author = { A. Treibergs }, Title = { {B}ounds on hyperspheres with prescribed {G}aussian curvature }, Journal = { J. Differential Geom. }, Volume = { 31 }, Pages = { 913-926 }, Year = { 1990 } } @Incollection{ Tre91, Author = { A. Treibergs }, Title = { {C}onstant mean curvature hypersurface of {M}inkowski space and related problems }, Booktitle = { {K}or. {A}dv. {I}nst. {S}ci. {T}ech. }, Address = { Korea }, Pages = { 95-158 }, Year = { 1991 } } @Article{ TreWei83, Author = { A. Treibergs and S.W. Wei }, Title = { {E}mbedded hyperspheres with prescribed mean curvature }, Journal = { J. Differential Geom. }, Volume = { 18 }, Pages = { 513-521 }, Year = { 1983 } } @Incollection{ Tri82, Author = { R. Tribuzy }, Title = { {S}uperficies minimas en {${C}{P}^2$} }, Booktitle = { {E}scola de geom. dif. {I}.{M}.{P}.{A}. }, Pages = { 93-97 }, Year = { 1982 } } @Unpublished{ Tro, Author = { A.J. Tromba }, Title = { {D}egree theory on oriented infinite dimensional varieties and the {M}orse number of minimal surfaces spanning a curve in {${\bf {R}}^n$}. {I}{I} }, Note = { preprint } } @Unpublished{ TroA, Author = { A.J. Tromba }, Title = { {O}n {P}lateau's problem for minimal surfaces of higher genus in {${\bf {R}}^n$} }, Note = { preprint } } @Book{ Tro77, Author = { A.J. Tromba }, Title = { {O}n the number of simply connected minimal surfaces spanning a curve }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 184 }, Series = { Mem.\ Amer.\ Math.\ Soc. }, Year = { 1977 } } @Article{ Tro83, Author = { A.J. Tromba }, Title = { {A} sufficient condition for a critical point of a functional to be a minimum and its application to {P}lateau's problem }, Journal = { Math.\ Ann. }, Volume = { 263 }, Pages = { 303-312 }, Year = { 1983 } } @Article{ Tro85, Author = { A.J. Tromba }, Title = { {D}egree theory on oriented infinite dimensional varieties and the {M}orse number of minimal surfaces spanning a curve in {${\bf {R}}^n$}. {I} }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 290 }, Pages = { 385-413 }, Year = { 1985 } } @Unpublished{ Tro87, Author = { A.J. Tromba }, Title = { {D}irichlet's energy and the {N}ielsen realization problem }, Note = { preprint, Max Planck Inst. }, Year = { 1987 } } @Article{ Tro87A, Author = { A.J. Tromba }, Title = { {O}n an energy function for the {W}eil--{P}etersson metric }, Journal = { Manuscripta Math. }, Volume = { 59 }, Pages = { 249-266 }, Year = { 1987 } } @Incollection{ Tro88, Author = { A.J. Tromba }, Title = { {O}pen problems in the degree theory for disc minimal surfaces spanning a curve in {${\bf {R}}^3$} }, Booktitle = { {P}artial {D}ifferential {E}quations and {C}alculus of {V}ariations }, Editor = { S. Hildebrandt and R. Leis }, Publisher = { Springer }, Volume = { 1357 }, Pages = { 379-401 }, Series = { Lecture Notes in Math. }, Year = { 1988 } } @Article{ Tro90, Author = { A.J. Tromba }, Title = { {A} new proof that {T}eichm\"uller space is a complex {S}tein manifold }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 303 }, Pages = { 257-262 }, Year = { 1990 } } @Unpublished{ Tro92, Author = { A.J. Tromba }, Title = { {D}irichlet's energy on {T}eichm\"uller's moduli space is strictly pluri-subharmonic }, Note = { SFB256 Bonn }, Year = { 1992 } } @Unpublished{ Tro92A, Author = { A.J. Tromba }, Title = { {O}n the {L}evi form of {D}irichlet's energy on {T}eichm\"uller's moduli space }, Note = { SFB256 Bonn }, Year = { 1992 } } @Book{ Tro92B, Author = { A.J. Tromba }, Title = { {T}eichm\"uller theory in {R}iemannian geometry }, Publisher = { Birh\"auser }, Address = { Boston }, Series = { ETH Lectures in Mathematics }, Year = { 1992 } } @Article{ Tro93, Author = { A.J. Tromba }, Title = { {I}ntrinsic third derivatives for {P}lateau's problem and the {M}orse inequalities for disc minimal surfaces in {${\bf {R}}^3$} }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 1 }, Pages = { 335-353 }, Year = { 1993 } } @Article{ Tsa91, Author = { I.H. Tsai }, Title = { {R}igidity of holomorphic maps between compact {H}ermitian symmetric spaces }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 717-729 }, Year = { 1991 } } @Unpublished{ Tsu, Author = { H. Tsuji }, Title = { {H}armonic maps into noncompact {K}\"ahler manifolds }, Note = { preprint } } @Unpublished{ TsuA, Author = { H. Tsuji }, Title = { {S}trong rigidity of negatively curved {K}\"ahler manifolds of finite volume }, Note = { preprint } } @Article{ Tsu82, Author = { T. Tsujishita }, Title = { {O}n variation bicomplexes associated to differential equations }, Journal = { Osaka J. Math. }, Volume = { 19 }, Pages = { 311-363 }, Year = { 1982 } } @Article{ Tsu83, Author = { K. Tsukada }, Title = { {I}sotropic minimal immersions of spheres into spheres }, Journal = { J. Math.\ Soc.\ Japan }, Volume = { 35 }, Pages = { 355-379 }, Year = { 1983 } } @Article{ Tul77, Author = { W.M. Tulczyjew }, Title = { {T}he {L}agrange complex }, Journal = { Bull.\ Soc.\ Math.\ France }, Volume = { 105 }, Pages = { 419-431 }, Year = { 1977 } } @Incollection{ Tul80, Author = { W.M. Tulczyjew }, Title = { {T}he {E}uler--{L}agrange resolution }, Booktitle = { {D}ifferential geometric methods in {M}athematical {P}hysics }, Editor = { P.L. Garc{\'\i}a and A. Perez-Mendon and J.-M. Souriau }, Publisher = { Springer }, Address = { Berlin }, Volume = { 836 }, Pages = { 22-48 }, Series = { Lecture Notes in Math. }, Year = { 1980 } } @Article{ Tul88, Author = { W.M. Tulczyjew }, Title = { {C}ohomology of the {L}agrange complex }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Pages = { 217-227 }, Year = { 1988 } } @Article{ Tuz91, Author = { A.A. Tuzhilin }, Title = { {M}orse-type indices of two dimensional minimal surfaces in {${R}^3$} and {${H}^3$} }, Journal = { Izv.\ Akad.\ Nauk SSSR Ser.\ Mat. }, Volume = { 55 }, Year = { 1991 } } @Incollection{ Tuz93, Author = { A.A. Tuzhilin }, Title = { {G}lobal properties of minimal surfaces in {${\bf {R}}^3$} and {${\bf {H}}^3$} and their {M}orse type indices }, Booktitle = { {M}inimal surfaces }, Publisher = { American Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 15 }, Series = { Adv.\ Soviet Math. }, Year = { 1993 } } @Article{ Tyr84, Author = { A.V. Tyrin }, Title = { {C}ritical points of the multidimensional {D}irichlet functional }, Journal = { Mat.\ Sb. }, Volume = { 124 }, Pages = { 146-158 }, Year = { 1984 } } @Article{ Tyr84A, Author = { A.V. Tyrin }, Title = { {T}he property of absence of local minima in the multidimensional {D}irichlet functional }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 39 }, Number = { 2 }, Pages = { 193-194 }, Year = { 1984 } } @Incollection{ Tyr86, Author = { A.V. Tyrin }, Title = { {A} problem of the minimization of functionals of {D}irichlet type }, Booktitle = { {G}eometry, differential equations and mechanics }, Publisher = { Moskov.\ Gos.\ Univ.\ Mekh.-Mat.\ Fak. }, Address = { Moscow }, Pages = { 145-150 }, Note = { (Russian) }, Year = { 1986 } } @Article{ Tyr87, Author = { A.V. Tyrin }, Title = { {R}egularity of harmonic mappings as a consequence of an instability property }, Journal = { Dokl.\ Akad.\ Nauk SSSR }, Volume = { 294 }, Pages = { 1306-1309 }, Year = { 1987 } } @Article{ Tyr87A, Author = { A.V. Tyrin }, Title = { {R}egularity of the mappings of {R}iemannian manifolds minimizing a multidimensional {D}irichlet functional }, Journal = { Mat.\ Sb. }, Volume = { 132 }, Pages = { 401-419 }, Year = { 1987 } } @Article{ Tyr91, Author = { A.V. Tyrin }, Title = { {H}armonic spheres in compact {L}ie groups and extremals of a multivalued {N}ovikov functional }, Journal = { Uspekhi Mat.\ Nauk }, Volume = { 46 }, Number = { 3 }, Pages = { 197-198 }, Year = { 1991 } } @Article{ Tyr91A, Author = { A.V. Tyrin }, Title = { {O}n the zero curvature representation for harmonic mappings into compact {L}ie groups }, Journal = { Trudy Sem.\ Vektor.\ Tenzor.\ Anal. }, Volume = { 24 }, Pages = { 199-207 }, Note = { (Russian) }, Year = { 1991 } } @Incollection{ Tyr93, Author = { A.V. Tyrin }, Title = { {O}n the {D}irichlet problem for harmonic maps }, Booktitle = { {T}opology and its {A}pplications }, Editor = { S.P. Novikov }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 193 }, Pages = { 209-211 }, Series = { Proc.\ Steklov Inst.\ Math. }, Year = { 1993 } } @Article{ Tys87, Author = { J. Tysk }, Title = { {E}igenvalue estimates with applications to minimal surfaces }, Journal = { Pacific J. Math. }, Volume = { 128 }, Pages = { 361-366 }, Year = { 1987 } } @Article{ Tys89, Author = { J. Tysk }, Title = { {F}initeness of index and total scalar curvature for minimal hypersurfaces }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 105 }, Year = { 1989 } } @Article{ Ucc, Author = { J. Ucci }, Title = { {O}n the non-existence of {R}iemannian submersions from {${C}{P}(7)$} and {${Q}{P}(3)$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 88 }, Pages = { 698-700 } } @Article{ Uch80, Author = { F. Uchida }, Title = { {A}n orthogonal transformation group of {$(8k-1)$}-sphere }, Journal = { J. Differential Geom. }, Volume = { 15 }, Pages = { 569-574 }, Year = { 1980 } } @Article{ Uda84, Author = { T. Uda }, Title = { {O}n global solution of {E}ells--{S}ampson equation into the two sphere {${S}^2$} }, Journal = { J. Fac.\ Sci.\ Univ.\ Tokyo Sect.\ IA Math. }, Volume = { 31 }, Pages = { 351-372 }, Year = { 1984 } } @Article{ Uda87, Author = { S. Udagawa }, Title = { {M}inimal immersions of {K}aehler manifolds in complex space forms }, Journal = { Tokyo J. Math. }, Volume = { 10 }, Pages = { 227-239 }, Year = { 1987 } } @Article{ Uda88, Author = { S. Udagawa }, Title = { {H}olomorphicity of certain stable harmonic maps and minimal immersions }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 57 }, Pages = { 577-598 }, Year = { 1988 } } @Article{ Uda88A, Author = { S. Udagawa }, Title = { {P}luriharmonic maps and minimal immersions of {K}aehler manifolds }, Journal = { J. London Math.\ Soc. }, Volume = { 37 }, Pages = { 375-384 }, Year = { 1988 } } @Article{ Uda94, Author = { S. Udagawa }, Title = { {C}lassification of pluriharmonic maps from compact complex manifolds with positive first {C}hern class into complex {G}rassmann manifolds }, Journal = { T\^ohoku Math.\ J. }, Volume = { 46 }, Pages = { 367-391 }, Year = { 1994 } } @Unpublished{ Uda94A, Author = { S. Udagawa }, Title = { {H}armonic tori in quaternionic projective {$3$}-spaces }, Note = { Preprint }, Year = { 1994 } } @Article{ Uda95, Author = { S. Udagawa }, Title = { {H}armonic maps from a two-torus into a complex {G}rassmann manifold }, Journal = { Internat.\ J. Math. }, Volume = { 6 }, Pages = { 447-459 }, Year = { 1995 } } @Article{ Uen93, Author = { K. Ueno }, Title = { {S}ome new examples of eigenmaps from {${S}^m$} into {${S}^n$} }, Journal = { Proc.\ Japan Acad.\ Ser.\ A Math.\ Sci. }, Volume = { 69 }, Pages = { 205-208 }, Year = { 1993 } } @Article{ Uen94, Author = { K. Ueno }, Title = { {A} study of ordinary differential equations arising from equivariant harmonic maps }, Journal = { Tokyo J. Math. }, Volume = { 17 }, Pages = { 395-416 }, Year = { 1994 } } @Article{ UenUra94, Author = { K. Ueno and H. Urakawa }, Title = { {E}quivariant harmonic maps associated to large group actions }, Journal = { Tokyo J. Math. }, Volume = { 17 }, Pages = { 417-437 }, Year = { 1994 } } @Unpublished{ Uhl, Author = { K. Uhlenbeck }, Title = { {H}armonic maps }, Note = { Founders Day Lecture, Stony Brook } } @Article{ Uhl70, Author = { K. Uhlenbeck }, Title = { {H}armonic maps : {A} direct method in the calculus of variations }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 76 }, Pages = { 1082-1987 }, Year = { 1970 } } @Unpublished{ Uhl75, Author = { K. Uhlenbeck }, Title = { {M}inimal {$2$}-spheres and tori in {${S}^k$} }, Note = { preprint }, Year = { 1975 } } @Article{ Uhl77, Author = { K. Uhlenbeck }, Title = { {R}egularity for a class of non-linear elliptic systems }, Journal = { Acta Math. }, Volume = { 138 }, Pages = { 219-240 }, Year = { 1977 } } @Article{ Uhl81, Author = { K. Uhlenbeck }, Title = { {M}orse theory by perturbation methods with applications to harmonic maps }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 267 }, Pages = { 569-583 }, Year = { 1981 } } @Article{ Uhl82, Author = { K. Uhlenbeck }, Title = { {C}onnnections with {${L}^p$} bounds on curvature }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 83 }, Pages = { 31-42 }, Year = { 1982 } } @Incollection{ Uhl82A, Author = { K. Uhlenbeck }, Title = { {E}quivariant harmonic maps into spheres }, Booktitle = { {H}armonic {M}aps }, Editor = { R.J. Knill and M. Kalka and H.C.J. Sealey }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 949 }, Pages = { 146-158 }, Series = { Lecture Notes in Math. }, Year = { 1982 } } @Article{ Uhl82B, Author = { K. Uhlenbeck }, Title = { {R}emovable singularities in {Y}ang--{M}ills fields }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 83 }, Pages = { 11-29 }, Year = { 1982 } } @Incollection{ Uhl82C, Author = { K. Uhlenbeck }, Title = { {V}ariational problems for gauge fields }, Booktitle = { {S}eminar on {D}ifferential {G}eometry }, Editor = { S.T. Yau }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 102 }, Pages = { 455-464 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1982 } } @Incollection{ Uhl83, Author = { K. Uhlenbeck }, Title = { {C}losed minimal hypersurfaces in hyperbolic {$3$}-manifolds }, Booktitle = { {S}eminar on {M}inimal {S}urfaces }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 103 }, Pages = { 147-168 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Incollection{ Uhl83A, Author = { K. Uhlenbeck }, Title = { {C}onservation laws and their application in global differential geometry }, Booktitle = { {E}mmy {N}oether in {B}ryn {M}awr }, Editor = { B. Srinavasan and J.D. Sally }, Publisher = { Springer }, Address = { Berlin }, Pages = { 103-115 }, Year = { 1983 } } @Incollection{ Uhl83B, Author = { K. Uhlenbeck }, Title = { {M}inimal spheres and other conformal variational problems }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, N.J. }, Volume = { 103 }, Pages = { 169-176 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Incollection{ Uhl83C, Author = { K. Uhlenbeck }, Title = { {V}ariational problems for gauge fields }, Booktitle = { {P}roc. {I}.{C}.{M}. {W}arsaw }, Pages = { 585-591 }, Year = { 1983 } } @Incollection{ Uhl84, Author = { K. Uhlenbeck }, Title = { {V}ariational problems in non-abelian gauge theories }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei, 1981 }, Publisher = { Sci.\ Press }, Address = { Beijing }, Pages = { 443-471 }, Year = { 1984 } } @Article{ Uhl89, Author = { K. Uhlenbeck }, Title = { {H}armonic maps into {L}ie groups. ({C}lassical solutions of the chiral model) }, Journal = { J. Differential Geom. }, Volume = { 30 }, Pages = { 1-50 }, Year = { 1989 } } @Article{ Uhl92, Author = { K. Uhlenbeck }, Title = { {O}n the connection between harmonic maps and the self-dual {Y}ang--{M}ills and sine {G}ordon equations }, Journal = { J. Geom.\ Phys. }, Volume = { 8 }, Pages = { 283-316 }, Year = { 1992 } } @Misc{ Ume, Author = { M. Umehara }, Title = { {C}omplete surfaces of constant mean curvature {$1$} in the hyperbolic space } } @Article{ Ume90, Author = { M. Umehara }, Title = { {A} characterization of compact surfaces with constant mean curvature }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 108 }, Pages = { 483-489 }, Year = { 1990 } } @Misc{ UmeYam, Author = { M. Umehara and K. Yamada }, Title = { {G}auss maps of compact surfaces with constant mean curvature } } @Unpublished{ UmeYamA, Author = { M. Umehara and K. Yamada }, Title = { {T}he moduli of surfaces of constant mean curvature {$c$} in {${H}^3(-c^2)$} with prescribed hyperbolic {G}auss map }, Note = { Preprint } } @Incollection{ UmeYam89, Author = { M. Umehara and K. Yamada }, Title = { {H}armonic non-holomorphic mappings of {$2$}-tori into the {$2$}-spheres }, Booktitle = { {G}eometry of manifolds }, Editor = { K. Shiohama }, Publisher = { Acad.\ Press }, Address = { San Diego }, Volume = { 8 }, Pages = { 151-161 }, Series = { Perspect.\ Math. }, Year = { 1989 } } @Article{ UmeYam92, Author = { M. Umehara and K. Yamada }, Title = { {A} parametrization of the {W}eierstrass formulae and perturbation of complete minimal surfaces in {${\bf {R}}^3$} into the hyperbolic {$3$}-space }, Journal = { J. Reine Angew.\ Math. }, Volume = { 432 }, Pages = { 93-116 }, Year = { 1992 } } @Misc{ Ura, Author = { H. Urakawa }, Title = { {S}pectrum of the {J}acobi operator on a minimal hypersurface of the {E}uclidean space } } @Article{ Ura84, Author = { H. Urakawa }, Title = { {N}umerical computations of the spectra of the {L}aplacian on {$7$}-dimensional homogeneous manifolds {${S}{U}(3)/{T}(k,l)$} }, Journal = { SIAM J. Math.\ Anal. }, Volume = { 15 }, Pages = { 979-987 }, Year = { 1984 } } @Article{ Ura85, Author = { H. Urakawa }, Title = { {M}inimal immersions of projective spaces into spheres }, Journal = { Tsukuba J. Math. }, Volume = { 9 }, Pages = { 321-367 }, Year = { 1985 } } @Article{ Ura86, Author = { H. Urakawa }, Title = { {T}he first eigenvalue of the {L}aplacian for a positively curved homogeneous {R}iemannian manifold }, Journal = { Compositio Math. }, Volume = { 59 }, Pages = { 57-71 }, Year = { 1986 } } @Article{ Ura86A, Author = { H. Urakawa }, Title = { {S}pectra of some domains in compact {L}ie groups and their applications }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 97 }, Pages = { 717-723 }, Year = { 1986 } } @Incollection{ Ura86B, Author = { H. Urakawa }, Title = { {S}tability of harmonic maps and eigenvalues of the {L}aplacian }, Booktitle = { {C}urvature and topology of {R}iemannian manifolds }, Editor = { K. Shiohama and T. Sakai and T. Sunada }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1201 }, Pages = { 285-307 }, Series = { Lecture Notes in Math. }, Year = { 1986 } } @Article{ Ura87, Author = { H. Urakawa }, Title = { {S}tability of harmonic maps and eigenvalues of the {L}aplacian }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 301 }, Pages = { 557-589 }, Year = { 1987 } } @Article{ Ura88, Author = { H. Urakawa }, Title = { {S}tability for harmonic mappings }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Journal = { Sugaku Expositions }, Volume = { 1 }, Pages = { 1-25 }, Year = { 1988 } } @Article{ Ura89, Author = { H. Urakawa }, Title = { {S}pectral geometry of the second variation operator of harmonic maps }, Journal = { Illinois J. Math. }, Volume = { 33 }, Pages = { 250-267 }, Year = { 1989 } } @Incollection{ Ura91, Author = { H. Urakawa }, Title = { {G}eometry of the {L}aplace-{B}eltrami operator on a complete {R}iemannian manifold }, Booktitle = { {R}ecent {D}evelopments in {D}ifferential {G}eometry }, Volume = { 22 }, Pages = { 1-58 }, Series = { Adv.\ Stud.\ Pure Math. }, Year = { 1991 } } @Book{ Ura93, Author = { H. Urakawa }, Title = { {C}alculus of {V}ariations and {H}armonic {M}aps }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 132 }, Series = { Transl.\ Math.\ Monographs }, Year = { 1993 } } @Article{ Ura93A, Author = { H. Urakawa }, Title = { {E}quivariant harmonic maps between compact {R}iemannian manifolds of cohomogeneity one }, Journal = { Michigan Math.\ J. }, Volume = { 40 }, Pages = { 27-51 }, Year = { 1993 } } @Article{ Urb85, Author = { F. Urbano }, Title = { {T}otally real minimal submanifolds of a complex projective space }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 93 }, Pages = { 332-334 }, Year = { 1985 } } @Article{ Urb90, Author = { F. Urbano }, Title = { {M}inimal surfaces with low index in the three dimensional sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 108 }, Pages = { 989-992 }, Year = { 1990 } } @Article{ Urb93, Author = { F. Urbano }, Title = { {I}ndex of {L}agrangian submanfolds of {${\bf {C}}{P}^n$} and the {L}aplacian of {$1$}-forms }, Journal = { Geom.\ Dedicata }, Volume = { 48 }, Pages = { 309-318 }, Year = { 1993 } } @Incollection{ Vai83, Author = { I. Vaisman }, Title = { {A} {S}chwarz lemma for complex surfaces }, Booktitle = { {G}lobal {A}nal. (in memory {M}. {M}orse) }, Editor = { T.M. Rassias }, Publisher = { Teubner }, Pages = { 305-323 }, Year = { 1983 } } @Article{ Vai85, Author = { I. Vaisman }, Title = { {S}ymplectic curvature tensors }, Journal = { Monatsh.\ Math. }, Volume = { 100 }, Pages = { 299-327 }, Year = { 1985 } } @Article{ Vai87, Author = { I. Vaisman }, Title = { {S}ymplectic twistor spaces }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 99 }, Pages = { 507-524 }, Year = { 1987 } } @Article{ Val87, Author = { G. Valli }, Title = { {S}ome remarks on geodesics in gauge groups and harmonic maps }, Journal = { J. Geom.\ Phys. }, Volume = { 4 }, Pages = { 335-359 }, Year = { 1987 } } @Article{ Val88, Author = { G. Valli }, Title = { {O}n the energy spectrum of harmonic {$2$}-spheres in unitary groups }, Journal = { Topology }, Volume = { 27 }, Pages = { 129-136 }, Year = { 1988 } } @Unpublished{ Val88A, Author = { G. Valli }, Title = { {S}ome aspects of the theory of harmonic gauges over {R}iemann surfaces }, Note = { Warwick Thesis }, Year = { 1988 } } @Article{ Val89, Author = { G. Valli }, Title = { {H}armonic gauges on {R}iemann surfaces and stable bundles }, Journal = { Ann.\ Inst.\ H. Poincar\'e.\ Anal.\ Non Lin\'eaire }, Volume = { 6 }, Pages = { 233-245 }, Year = { 1989 } } @Article{ Val93, Author = { G. Valli }, Title = { {H}olomorphic maps from compact manifolds into loop groups as {B}laschke products }, Journal = { T\^ohoku Math.\ J. }, Volume = { 45 }, Pages = { 393-422 }, Year = { 1993 } } @Article{ Val94, Author = { G. Valli }, Title = { {I}nterpolation theory, loop groups and instantons }, Journal = { J. Reine Angew.\ Math. }, Volume = { 446 }, Pages = { 137-163 }, Year = { 1994 } } @Article{ Van90, Author = { A.-J. Vanderwinden }, Title = { {T}otally geodesic spheres in complex {G}rassmannians and unitary groups }, Journal = { Simon Stevin }, Volume = { 64 }, Pages = { 285-298 }, Year = { 1990 } } @Unpublished{ Van92, Author = { A.-J. Vanderwinden }, Title = { {E}xemples d'applications harmoniques }, Note = { Th\`ese Univ. Libre Bruxelles }, Year = { 1992 } } @Article{ Van93, Author = { A.-J. Vanderwinden }, Title = { {E}xamples of harmonic mappings obtained by reduction }, Journal = { Bull.\ London Math.\ Soc. }, Volume = { 25 }, Pages = { 282-288 }, Year = { 1993 } } @Article{ VanVaz88, Author = { L. Vanhecke and M.E. Vazquez-Abal }, Title = { {H}armonic reflections }, Journal = { Atti Accad.\ Naz.\ Lincei Rend.\ Cl.\ Sci.\ Fis.\ Mat.\ Natur.\ (8) }, Volume = { 82 }, Pages = { 229-236 }, Year = { 1988 } } @Incollection{ Van90A, Author = { I. Van~de~Woestijne }, Title = { {M}inimal surfaces of the {$3$}-dimensional {M}inkowski space }, Booktitle = { {G}eo. \& topology of submanifolds {I}{I} }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 344-369 }, Year = { 1990 } } @Article{ Var86, Author = { N.T. Varopoulos }, Title = { {I}nformation theory and harmonic functions }, Journal = { Bull.\ Sci.\ Math }, Volume = { 110 }, Pages = { 347-389 }, Year = { 1986 } } @Incollection{ Vaz91, Author = { M.E. Vazquez-Abal }, Title = { {H}armonicity and {B}rownian motion }, Booktitle = { {P}roc. {W}orkshop on {R}ecent {T}opics in {D}ifferential {G}eometry, {P}uerto de la {C}ruz ({T}enerife, {S}pain) }, Publisher = { Univ.\ La Laguna }, Volume = { 32 }, Pages = { 123-132 }, Series = { Secret.\ Public.\ Univ.\ de La Laguna Serie Informes }, Year = { 1991 } } @Article{ Vaz91A, Author = { M.E. Vazquez-Abal }, Title = { {H}armonicit\'e sur le fibr\'e tangent d'ordre {$r$} }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 321 }, Pages = { 131-136 }, Year = { 1991 } } @Misc{ Vel, Author = { J.A. Velling }, Title = { {E}xistence and uniqueness of complete constant mean curvature surfaces at infinity of {${H}^3$} } } @Incollection{ Ver83, Author = { J.-L. Verdier }, Title = { {T}wo dimensional {$\sigma$}-models and harmonic maps from {${S}^2$} to {${S}^{2n}$} }, Booktitle = { {G}roup {T}heoretical {M}ethods in {P}hysics }, Editor = { M. Serdaro{\u g}lu and E. {\'I}n{\"o}n{\"u} }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 180 }, Pages = { 136-141 }, Series = { Lecture Notes in Phys. }, Year = { 1983 } } @Incollection{ Ver85, Author = { J.-L. Verdier }, Title = { {A}pplications harmoniques de {${S}^2$} dans {${S}^4$} }, Booktitle = { {G}eometry {T}oday }, Editor = { E. Arbarello and C. Procesi and E. Strickland }, Publisher = { Birkh\"auser }, Address = { Boston }, Volume = { 60 }, Pages = { 267-282 }, Series = { Progr.\ Math. }, Year = { 1985 } } @Incollection{ Ver88, Author = { J.-L. Verdier }, Title = { {A}pplications harmoniques de {${S}^2$} dans {${S}^4$} {I}{I} }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 124-147 }, Year = { 1988 } } @Misc{ Vil, Author = { M. Ville }, Title = { {T}he contribution of branch points to the twistor degree of minimal surfaces in compact {R}iemannian 4-manifolds } } @Article{ Vil91, Author = { M. Ville }, Title = { {T}wistor examples of algebraic dimension zero threefolds }, Journal = { Invent.\ Math. }, Volume = { 103 }, Pages = { 537-546 }, Year = { 1991 } } @Article{ Vil93, Author = { M. Ville }, Title = { {H}armonic maps, second homotopy classes of smooth manifolds, and bounded cohomology }, Journal = { Internat.\ J. Math. }, Volume = { 4 }, Pages = { 997-1006 }, Year = { 1993 } } @Unpublished{ Vil67, Author = { J. Vilms }, Title = { {C}onnections and maps }, Note = { Columbia Univ. Ph.D Thesis }, Year = { 1967 } } @Article{ Vil67A, Author = { J. Vilms }, Title = { {C}onnections on tangent bundles }, Journal = { J. Differential Geom. }, Volume = { 1 }, Pages = { 235-243 }, Year = { 1967 } } @Article{ Vil70, Author = { J. Vilms }, Title = { {T}otally geodesic maps }, Journal = { J. Differential Geom. }, Volume = { 4 }, Pages = { 73-79 }, Year = { 1970 } } @Article{ Vil72, Author = { J. Vilms }, Title = { {S}ubmanifolds of {E}uclidean space with parallel second fundamental form }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 32 }, Pages = { 263-267 }, Year = { 1972 } } @Article{ Vin78, Author = { A.M. Vinogradov }, Title = { {A} spectral sequence that is connected with a nonlinear differential equation and the algebraic-geometry foundations of the {L}agrange field theory with constraints }, Journal = { Soviet Math.\ Dokl. }, Volume = { 19 }, Pages = { 114-118 }, Year = { 1978 } } @Article{ Vin84, Author = { A.M. Vinogradov }, Title = { {T}he {${C}$}-spectral sequence, {L}agrangian formalism and conservation laws {I}, {I}{I} }, Journal = { J. Math.\ Anal.\ Appl. }, Volume = { 100 }, Pages = { 1-129 }, Year = { 1984 } } @Article{ Vis82, Author = { M. Visinescu }, Title = { {N}ew instanton and meron solutions of a generally covariant four dimensional sigma model }, Journal = { Z. Phys. }, Volume = { C15 }, Pages = { 121-127 }, Year = { 1982 } } @Article{ Vis87, Author = { M. Visinescu }, Title = { {M}assless {K}aluza-{K}lein gauge fields and space-time compactification induced by scalars }, Journal = { Europhys.\ Lett. }, Volume = { 4 }, Pages = { 767-770 }, Year = { 1987 } } @Article{ von81, Author = { W. von~Wahl }, Title = { {K}lassische {L}\"osbarkeit im {G}rossen f\"ur nichlineare parabolische {S}ysteme und das {V}erhalten der {L}\"osungen f\"ur {$t\rightarrow\infty$} }, Journal = { Nachr.\ Akad.\ Wiss.\ G\"ottingen Math.-Phys.\ Kl.\ II }, Volume = { 5 }, Pages = { 131-177 }, Year = { 1981 } } @Book{ Vai71, Author = { J. V{\"a}is{\"a}l{\"a} }, Title = { {L}ectures on {$n$}-dimensional quasiconformal mappings }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 229 }, Series = { Lecture Notes in Math. }, Year = { 1971 } } @Article{ Wal70, Author = { N.R. Wallach }, Title = { {E}xtension of locally defined minimal immersions of spheres into spheres }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 21 }, Pages = { 210-213 }, Year = { 1970 } } @Incollection{ Wal72, Author = { N.R. Wallach }, Title = { {M}inimal immersions of symmetric space into spheres }, Booktitle = { {S}ymmetric spaces }, Publisher = { M. Dekker }, Address = { New York }, Pages = { 1-40 }, Year = { 1972 } } @Misc{ Wal, Author = { R. Walter }, Title = { {E}xplicit examples to the {${H}$}-problem of {H}einz {H}opf } } @Article{ Wal81, Author = { R. Walter }, Title = { {K}onvexit\"at in riemannschen {M}annigfaltigkeiten }, Journal = { J. Deutsch.\ Math.\ Verein. }, Volume = { 83 }, Pages = { 1-31 }, Year = { 1981 } } @Article{ Wan92, Author = { T.Y.H. Wan }, Title = { {C}onstant mean curvature surface, harmonic maps and universal {T}eichm\"uller space }, Journal = { J. Differential Geom. }, Volume = { 35 }, Pages = { 643-657 }, Year = { 1992 } } @Article{ Wan85, Author = { A.N. Wang }, Title = { {H}armonic coframes on {R}iemannian manifolds }, Journal = { Chinese J. Math. }, Volume = { 13 }, Pages = { 187-194 }, Year = { 1985 } } @Article{ Wan87, Author = { B.W. Wang }, Title = { {S}ubmanifolds in {${S}^{N}$} with constant mean curvature }, Journal = { Hunan Ann.\ Math. }, Volume = { 7 }, Pages = { 46-57 }, Year = { 1987 } } @Article{ Wan90, Author = { C.P. Wang }, Title = { {R}igidity theorems for harmonic maps from {R}iemannian manifold to {G}rassmannian manifold }, Journal = { Acta Math.\ Sinica }, Volume = { 6 }, Pages = { 297-305 }, Year = { 1990 } } @Article{ Wan92A, Author = { G.F. Wang }, Title = { {N}onsymmetric harmonic maps from annuli to {$2$}-sphere }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 315 }, Pages = { 699-702 }, Year = { 1992 } } @Article{ Wan93, Author = { G.F. Wang }, Title = { {H}armonic maps from a closed surface of higher genus to a {$2$}-sphere }, Journal = { Internat.\ J. Math. }, Volume = { 4 }, Pages = { 359-365 }, Year = { 1993 } } @Incollection{ Wan94, Author = { H. Wang }, Title = { {C}onstruction of harmonic maps from {${\bf {R}}^2$} and {${\bf {R}}^{1,1}$} to the 3-dimensional sphere. }, Booktitle = { {I}nterface between {P}hysics and {M}athematics, {H}angzhou 1993 }, Publisher = { World Scient.\ Publ. }, Pages = { 380-383 }, Year = { 1994 } } @Misc{ Wan, Author = { J.P. Wang }, Title = { {L}inear growth harmonic functions on complete manifolds } } @Unpublished{ Wan94A, Author = { J.P. Wang }, Title = { {T}he heat flow and harmonic maps between complete manifolds }, Note = { U.C. Irvine Thesis }, Year = { 1994 } } @Article{ Wan87A, Author = { Q.M. Wang }, Title = { {I}soparametric functions on {R}iemannian manifolds ({I}) }, Journal = { Math.\ Ann. }, Volume = { 277 }, Pages = { 639-646 }, Year = { 1987 } } @Incollection{ Wan88, Author = { Q.M. Wang }, Title = { {I}soparametric maps of {R}iemannian manifolds and their applications }, Booktitle = { {A}dv. in {S}ci. of {C}hina {M}ath. {V}ol.2 }, Publisher = { Sci.\ Press \& John Wiley }, Pages = { 79-103 }, Year = { 1988 } } @Article{ Wan88A, Author = { Q.M. Wang }, Title = { {O}n the topology of {C}lifford isoparametric hypersurfaces }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 55-66 }, Year = { 1988 } } @Article{ Wan90A, Author = { Q.M. Wang }, Title = { {O}n totally geodesic spheres in {G}rassmannians and {${O}(n)$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 108 }, Pages = { 811-815 }, Year = { 1990 } } @Article{ Wan94B, Author = { Q.M. Wang }, Title = { {O}n a class of minimal hypersurfaces in {${\bf {R}}^n$} }, Journal = { Math.\ Ann. }, Volume = { 298 }, Pages = { 207-251 }, Year = { 1994 } } @Incollection{ WanA, Author = { S.P. Wang }, Title = { {B}ernstein conjecture in hyperbolic geometry }, Booktitle = { {S}eminar on minimal submanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Series = { Ann.\ of Math.\ Stud. } } @Article{ Wan96, Author = { S.S. Wang }, Title = { {$p$}-{D}irichlet energy minimizing maps into a complete manifold }, Journal = { Michigan Math.\ J. }, Volume = { 43 }, Pages = { 33-49 }, Year = { 1996 } } @Article{ Wan96A, Author = { S.S. Wang }, Title = { {E}nergy minimizing sections of a fibre bundle }, Journal = { Illinois J. Math. }, Volume = { 40 }, Pages = { 281-292 }, Year = { 1996 } } @Article{ Wan94C, Author = { Y. Wang }, Title = { {H}armonic maps from noncompact {R}iemannian manifolds with nonnegative {R}icci curvature outside a compact set }, Journal = { Proc.\ Roy.\ Soc.\ Edinburgh Sect.\ A }, Volume = { 124 }, Pages = { 1259-1275 }, Year = { 1994 } } @Article{ Wan90B, Author = { Y.N. Wang }, Title = { {T}he stability of domain and the pinching of energy about harmonic map }, Journal = { Acta Math.\ Sinica }, Volume = { 6 }, Pages = { 57-64 }, Year = { 1990 } } @Article{ War85, Author = { R.S. Ward }, Title = { {S}lowly-moving lumps in the {${C}{P}^1$} model in {$2+1$} dimensions }, Journal = { Phys.\ Lett.\ B }, Volume = { 158 }, Pages = { 424-428 }, Year = { 1985 } } @Article{ War90, Author = { R.S. Ward }, Title = { {C}lassical solutions of the chiral model, unitons and holomorphic vector bundles }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 128 }, Pages = { 319-332 }, Year = { 1990 } } @Article{ War92, Author = { R.S. Ward }, Title = { {D}iscretization of integrable systems }, Journal = { Phys.\ Lett.\ A }, Volume = { 165 }, Pages = { 325-329 }, Year = { 1992 } } @Incollection{ War94, Author = { R.S. Ward }, Title = { {S}igma models in {$2+1$} dimensions }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { E23 }, Pages = { 193-202 }, Series = { Aspects of Math. }, Year = { 1994 } } @Article{ Wat72, Author = { B. Watson }, Title = { {T}he first {B}etti numbers of certain locally trivial fibre spaces }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 78 }, Pages = { 392-393 }, Year = { 1972 } } @Article{ Wat73, Author = { B. Watson }, Title = { {M}anifolds maps commuting with the {L}aplacian }, Journal = { J. Differential Geom. }, Volume = { 8 }, Pages = { 85-94 }, Year = { 1973 } } @Article{ Wat75, Author = { B. Watson }, Title = { {$\delta$}-commuting mappings and {B}etti numbers }, Journal = { T\^ohoku Math.\ J. }, Volume = { 27 }, Pages = { 135-152 }, Year = { 1975 } } @Article{ Wat76, Author = { B. Watson }, Title = { {A}lmost {H}ermitian submersions }, Journal = { J. Differential Geom. }, Volume = { 11 }, Pages = { 147-165 }, Year = { 1976 } } @Article{ Web84, Author = { S.M. Webster }, Title = { {M}inimal surfaces in {K}\"ahler surfaces }, Journal = { J. Differential Geom. }, Volume = { 20 }, Pages = { 463-470 }, Year = { 1984 } } @Article{ Web85, Author = { S.M. Webster }, Title = { {T}he {E}uler and {P}ontrjagin numbers of an {$n$}-manifold in {${\bf {C}}^n$} }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 60 }, Pages = { 193-216 }, Year = { 1985 } } @Incollection{ Web86, Author = { S.M. Webster }, Title = { {O}n the relation between {C}hern and {P}ontrjagin numbers }, Booktitle = { {C}omplex differential geometry and non-linear differential equations }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 49 }, Pages = { 135-143 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Article{ Wei92, Author = { F.S. Wei }, Title = { {S}ome existence and uniqueness theorems for doubly periodic minimal surfaces }, Journal = { Invent.\ Math. }, Volume = { 109 }, Pages = { 113-136 }, Year = { 1992 } } @Misc{ Wei, Author = { S.W. Wei }, Title = { {E}xistence and regularity of minimizing maps into strongly unstable manifolds } } @Article{ Wei83, Author = { S.W. Wei }, Title = { {A}n average process in the calculus of variations and the stability of harmonic maps }, Journal = { Bull.\ Inst.\ Math.\ Acad.\ Sinica }, Volume = { 11 }, Pages = { 469-475 }, Year = { 1983 } } @Incollection{ Wei86, Author = { S.W. Wei }, Title = { {G}eneralized idea of {S}ynge and its applications to topology and calculus of variations in positively curved manifolds }, Booktitle = { {N}onlinear functional analysis and its applications }, Editor = { F.E. Browder }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 45 Part 2 }, Pages = { 533-539 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1986 } } @Incollection{ Wei86A, Author = { S.W. Wei }, Title = { {L}iouville theorems for stable harmonic maps into either strongly unstable, or {$\delta$}-pinched, manifolds }, Booktitle = { {G}eometric measure theory and the calculus of variations }, Editor = { W.K. Allard and F.J. Almgren }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 44 }, Pages = { 405-412 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1986 } } @Article{ Wei88, Author = { S.W. Wei }, Title = { {P}lateau's problem in symmetric spaces }, Journal = { Nonlinear Anal. }, Volume = { 12 }, Pages = { 749-760 }, Year = { 1988 } } @Incollection{ Wei89, Author = { S.W. Wei }, Title = { {A}n extrinsic average variational method }, Booktitle = { {R}recent {D}evelopments in {G}eometry }, Editor = { S.Y. Cheng and H. Choi and R.E. Greene }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 101 }, Pages = { 55-78 }, Series = { Contemp.\ Math. }, Year = { 1989 } } @Incollection{ Wei92A, Author = { S.W. Wei }, Title = { {L}iouville theorems and regularity of minimizing harmonic maps into superstrongly unstable manifolds }, Booktitle = { {G}eometry and nonlinear partial differential equations }, Editor = { V. Oliker and A. Treibergs }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 127 }, Pages = { 131-154 }, Series = { Contemp.\ Math. }, Year = { 1992 } } @Incollection{ Wei96, Author = { S.W. Wei }, Title = { {T}he minima of the {$p$}-energy functional }, Booktitle = { {E}lliptic and parabolic methods in geometry ({M}inneapolis, {M}{N}, 1994) }, Publisher = { A.K. Peters }, Address = { Wellesley, MA }, Pages = { 171--203 }, Year = { 1996 } } @Article{ WeiYau94, Author = { S.W. Wei and C.M. Yau }, Title = { {R}egularity of {$p$}-energy minimizing maps and {$p$}-superstrongly unstable indices }, Journal = { J. Geom.\ Anal. }, Volume = { 4 }, Pages = { 247-272 }, Year = { 1994 } } @Article{ Wei78, Author = { J.L. Weiner }, Title = { {O}n a problem of {C}hen, {W}illmore et al. }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 27 }, Pages = { 19-35 }, Year = { 1978 } } @Unpublished{ WeiA, Author = { G. Weinstein }, Title = { {O}n the {D}irichlet problem for harmonic maps with prescribed singularities }, Note = { preprint } } @Article{ Wei96A, Author = { G. Weinstein }, Title = { {H}armonic maps with prescribed singularities into {H}adamard manifolds }, Journal = { Math.\ Res.\ Lett. }, Volume = { 3 }, Pages = { 835--844 }, Year = { 1996 } } @Article{ Wei96B, Author = { G. Weinstein }, Title = { {H}armonic maps with prescribed singularities on unbounded domains }, Journal = { Amer.\ J. Math. }, Volume = { 118 }, Pages = { 689--700 }, Year = { 1996 } } @Article{ Wei93, Author = { T. Weinstein }, Title = { {I}nextendible conformal realizations of {L}orentz surfaces in {M}inkowski 3-space }, Journal = { Michigan Math.\ J. }, Volume = { 40 }, Pages = { 545-559 }, Year = { 1993 } } @Article{ Wei70, Author = { B.M. Weinstock }, Title = { {A}n approximation theorem for {$\partial$}-closed forms of type {$(n,n-1)$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 26 }, Pages = { 625-628 }, Year = { 1970 } } @Article{ WeiXav87, Author = { A. Weitsman and F. Xavier }, Title = { {S}ome function theoretic properties of the {G}auss map for hyperbolic complete minimal surfaces }, Journal = { Michigan Math.\ J. }, Volume = { 34 }, Pages = { 275-283 }, Year = { 1987 } } @Article{ Wen69, Author = { H.C. Wente }, Title = { {A}n existence theorem for surfaces of constant mean curvature }, Journal = { J. Math.\ Anal.\ Appl. }, Volume = { 26 }, Pages = { 318-344 }, Year = { 1969 } } @Article{ Wen71, Author = { H.C. Wente }, Title = { {A} general existence theorem for surfaces of constant mean curvature }, Journal = { Math.\ Z. }, Volume = { 120 }, Pages = { 277-288 }, Year = { 1971 } } @Article{ Wen75, Author = { H.C. Wente }, Title = { {T}he differential equation {$\{D}elta x=2{H}x_u\wedge x_v$} with vanishing boundary values }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 50 }, Pages = { 131-137 }, Year = { 1975 } } @Article{ Wen80, Author = { H.C. Wente }, Title = { {L}arge solutions to the volume constrained {P}lateau problem }, Journal = { Arch.\ Rational Mech.\ Anal. }, Volume = { 75 }, Pages = { 59-77 }, Year = { 1980 } } @Article{ Wen86, Author = { H.C. Wente }, Title = { {C}ounterexample to a conjecture of {H}. {H}opf }, Journal = { Pacific J. Math. }, Volume = { 121 }, Pages = { 193-243 }, Year = { 1986 } } @Incollection{ Wen86A, Author = { H.C. Wente }, Title = { {T}wisted tori of constant mean curvature in {${\bf {R}}^3$} }, Booktitle = { {S}eminar of new results in non-linear {P}.{D}.{E}. }, Editor = { A.J. Tromba }, Publisher = { Max-Planck-Institut f\"ur Mathematik }, Address = { Bonn }, Volume = { 10 }, Series = { Aspects of Math. }, Year = { 1986 } } @Article{ Wen91, Author = { H.C. Wente }, Title = { {A} note on the stability theorem of {J}.{L}.~{B}arbosa and {M}.~do~{C}armo for closed surfaces of constant mean curvature }, Journal = { Pacific J. Math. }, Volume = { 147 }, Pages = { 375-379 }, Year = { 1991 } } @Book{ Wen92, Author = { H.C. Wente }, Title = { {C}onstant mean curvature immersion of {E}nneper type }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 478 }, Series = { Mem.\ Amer.\ Math.\ Soc. }, Year = { 1992 } } @Incollection{ Wen93, Author = { H.C. Wente }, Title = { {C}omplete immersions of constant mean curvature }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 497-512 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ Wer57, Author = { H. Werner }, Title = { {D}as {P}roblem von {D}ouglas f\"ur konstanter mittlerer {K}r\"ummung }, Journal = { Math.\ Ann. }, Volume = { 133 }, Pages = { 303-319 }, Year = { 1957 } } @Incollection{ Wes87, Author = { A. West }, Title = { {I}soparametric systems }, Booktitle = { {G}eo. \& {T}opology of {S}ubmanifolds, {L}uminy }, Publisher = { World Sci. }, Address = { Singapore }, Year = { 1987 } } @Misc{ Whi, Author = { B. White }, Title = { {A} strong minimax property of non-degenerate minimal submanifolds } } @Article{ Whi79, Author = { B. White }, Title = { {T}he structure of minimizing hypersurfaces mod. {$4$} }, Journal = { Invent.\ Math. }, Volume = { 53 }, Pages = { 45-58 }, Year = { 1979 } } @Article{ Whi83, Author = { B. White }, Title = { {E}xistence of least-area mappings of {${N}$}-dimensional domains }, Journal = { Ann.\ of Math. }, Volume = { 118 }, Pages = { 179-185 }, Year = { 1983 } } @Incollection{ Whi83A, Author = { B. White }, Title = { {R}egularity of area-minimizing hypersurfaces at boundaries with multiplicity }, Booktitle = { {S}eminar on {M}inimal {S}ubmanifolds }, Editor = { E. Bombieri }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton, NJ }, Volume = { 103 }, Pages = { 293-301 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1983 } } @Article{ Whi83B, Author = { B. White }, Title = { {T}angent cones to {$2$}-dimensional area-minimizing integral currents are unique }, Journal = { Duke Math.\ J. }, Volume = { 50 }, Pages = { 143-160 }, Year = { 1983 } } @Article{ Whi84, Author = { B. White }, Title = { {M}appings that minimize area in their homotopy classes }, Journal = { J. Differential Geom. }, Volume = { 20 }, Pages = { 433-446 }, Year = { 1984 } } @Article{ Whi85, Author = { B. White }, Title = { {H}omotopy classes in {S}obolev spaces and energy minimizing maps }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 13 }, Pages = { 166-168 }, Year = { 1985 } } @Article{ Whi86, Author = { B. White }, Title = { {I}nfima of energy functionals in homotopy classes of mappings }, Journal = { J. Differential Geom. }, Volume = { 23 }, Pages = { 127-142 }, Year = { 1986 } } @Article{ Whi87, Author = { B. White }, Title = { {C}omplete surfaces of finite total curvature }, Journal = { J. Differential Geom. }, Volume = { 26 }, Pages = { 315-316 }, Year = { 1987 } } @Article{ Whi87A, Author = { B. White }, Title = { {T}he space of {$m$}-dimensional surfaces that are stationary for a parametric elliptic integral }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 36 }, Pages = { 567-602 }, Year = { 1987 } } @Article{ Whi88, Author = { B. White }, Title = { {H}omotopy classes in {S}obolev spaces and the existence of energy minimizing maps }, Journal = { Acta Math. }, Volume = { 160 }, Pages = { 1-17 }, Year = { 1988 } } @Article{ Whi89, Author = { B. White }, Title = { {E}very three-sphere of positive {R}icci curvature contains a minimal embedded torus }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 21 }, Pages = { 71-75 }, Year = { 1989 } } @Article{ Whi89A, Author = { B. White }, Title = { {N}ew applications of mapping degrees to minimal surface theory }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 143-162 }, Year = { 1989 } } @Article{ Whi91, Author = { B. White }, Title = { {E}xistence of smooth embedded surfaces of prescribed genus that minimize parametric even elliptic functionals on {$3$}-manifolds }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 413-443 }, Year = { 1991 } } @Article{ Whi91A, Author = { B. White }, Title = { {T}he space of minimal submanifolds for varying {R}iemannian metrics }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 40 }, Pages = { 161-260 }, Year = { 1991 } } @Article{ Whi92, Author = { B. White }, Title = { {N}onunique tangent maps at isolated singularities of harmonic maps }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 26 }, Pages = { 125-129 }, Year = { 1992 } } @Article{ Whi92A, Author = { B. White }, Title = { {O}n the topological type of minimal submanifolds }, Journal = { Topology }, Volume = { 31 }, Pages = { 445-448 }, Year = { 1992 } } @Article{ Whi94, Author = { B. White }, Title = { {T}he bridge principle for stable minimal surfaces }, Journal = { Calc.\ Var.\ Partial Differential Equations }, Volume = { 2 }, Pages = { 405-425 }, Year = { 1994 } } @Article{ Whi94A, Author = { B. White }, Title = { {T}he bridge principle for unstable and for singular minimal surfaces }, Journal = { Comm.\ Anal.\ Geom. }, Volume = { 2 }, Pages = { 513-532 }, Year = { 1994 } } @Article{ Whi94B, Author = { B. White }, Title = { {P}artial regularity of mean-curvature hypersurfaces flowing by mean curvature }, Journal = { Internat.\ Math.\ Res.\ Notices }, Year = { 1994 } } @Article{ Wil86, Author = { G.H. Williams }, Title = { {S}olutions of the minimal surface equation---continuous and discontinuous at the boundary }, Journal = { Comm.\ Partial Differential Equations }, Volume = { 11 }, Pages = { 1439-1547 }, Year = { 1986 } } @Article{ Wil71, Author = { T.J. Willmore }, Title = { {M}ean curvature of {R}iemannian immersions }, Journal = { J. London Math.\ Soc. }, Volume = { 3 }, Pages = { 307-310 }, Year = { 1971 } } @Incollection{ Wil74, Author = { T.J. Willmore }, Title = { {M}inimal conformal immersions }, Booktitle = { {G}eometrie {D}ifferentielle }, Editor = { E. Vidal }, Publisher = { Springer }, Volume = { 392 }, Pages = { 111-120 }, Series = { Lecture Notes in Math. }, Year = { 1974 } } @Incollection{ Wil76, Author = { T.J. Willmore }, Title = { {T}he tension field of maps of {R}iemannian manifolds }, Booktitle = { {D}ifferential {G}eometry and {R}elativity, (volume in honour of {A}. {L}ichnerowicz) }, Publisher = { Reidel }, Pages = { 159-167 }, Year = { 1976 } } @Book{ Wil82, Author = { T.J. Willmore }, Title = { {T}otal curvature in {R}iemannian geometry }, Publisher = { Wiley }, Year = { 1982 } } @Article{ Wit84, Author = { E. Witten }, Title = { {N}on-abelian bosonization in two dimensions }, Journal = { Comm.\ Math.\ Phys. }, Volume = { 92 }, Pages = { 455-472 }, Year = { 1984 } } @Article{ Woh91, Author = { M. Wohlgemuth }, Title = { {H}igher genus minimal surfaces by growing handles out of a catenoid }, Journal = { Manuscripta Math. }, Volume = { 70 }, Pages = { 397-428 }, Year = { 1991 } } @Article{ Wol66, Author = { J.A. Wolf }, Title = { {S}urfaces of constant mean curvature }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 17 }, Pages = { 1103-1114 }, Year = { 1966 } } @Article{ Wol69, Author = { J.A. Wolf }, Title = { {T}he action of a real semisimple group on a complex flag manifold {I}: {O}rbit structure and holomorphic arc components }, Journal = { Bull.\ Amer.\ Math.\ Soc. }, Volume = { 75 }, Pages = { 1121-1237 }, Year = { 1969 } } @Misc{ Wol, Author = { M. Wolf }, Title = { {M}easured foliations and harmonic maps of surfaces } } @Unpublished{ Wol86, Author = { M. Wolf }, Title = { {T}he {T}eichm\"uller theory of harmonic maps }, Note = { Doctoral Thesis Stanford }, Year = { 1986 } } @Article{ Wol89, Author = { M. Wolf }, Title = { {T}he {T}eichm\"uller theory of harmonic maps }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 449-479 }, Year = { 1989 } } @Article{ Wol91, Author = { M. Wolf }, Title = { {H}igh energy degeneration of harmonic maps between surfaces and rays in {T}eichm\"uller space }, Journal = { Topology }, Volume = { 30 }, Pages = { 517-540 }, Year = { 1991 } } @Article{ Wol91A, Author = { M. Wolf }, Title = { {I}nfinite energy harmonic maps and degeneration of hyperbolic surfaces in moduli space }, Journal = { J. Differential Geom. }, Volume = { 33 }, Pages = { 487-539 }, Year = { 1991 } } @Incollection{ Wol92, Author = { M. Wolf }, Title = { {H}armonic maps from a surface and degeneration in {T}eichm\"uller space }, Booktitle = { {P}roc. {L}ow {D}im. {T}op }, Pages = { 217-239 }, Year = { 1992 } } @Article{ Wol95, Author = { M. Wolf }, Title = { {H}armonic maps from surfaces to {${R}$}-trees }, Journal = { Math.\ Z. }, Volume = { 218 }, Pages = { 577-593 }, Year = { 1995 } } @Article{ Wol95A, Author = { M. Wolf }, Title = { {H}armonic maps from surfaces to {${R}$}-trees }, Journal = { Math.\ Z. }, Volume = { 218 }, Pages = { 577-594 }, Year = { 1995 } } @Article{ Wol95B, Author = { M. Wolf }, Title = { {O}n the existence of {J}enkins-{S}trebel differentials using harmonic maps from surfaces to graphs }, Journal = { Ann.\ Acad.\ Sci.\ Fenn.\ Ser.\ A I Math. }, Volume = { 20 }, Pages = { 269-278 }, Year = { 1995 } } @Article{ WolWol, Author = { M. Wolf and S. Wolpert }, Title = { {R}eal analytic structure on the moduli space of curves }, Journal = { Amer.\ J. Math. } } @Unpublished{ WolZwi92, Author = { M. Wolf and B. Zwiebach }, Title = { {T}he plumbing of minimal area surfaces }, Note = { Preprint }, Year = { 1992 } } @Unpublished{ Wol82, Author = { J.G. Wolfson }, Title = { {M}inimal surfaces in complex manifolds }, Note = { Univ. of California at Berkeley Ph.D Thesis }, Year = { 1982 } } @Article{ Wol85, Author = { J.G. Wolfson }, Title = { {O}n minimal surfaces in {K}\"ahler manifolds of constant holomorphic sectional curvature }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 290 }, Pages = { 627-646 }, Year = { 1985 } } @Article{ Wol85A, Author = { J.G. Wolfson }, Title = { {O}n minimal two-spheres in {K}\"ahler manifolds of constant holomorphic sectional curvature }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 290 }, Pages = { 627-646 }, Year = { 1985 } } @Article{ Wol86A, Author = { J.G. Wolfson }, Title = { {H}armonic maps of the two-sphere into the complex hyperquadric }, Journal = { J. Differential Geom. }, Volume = { 24 }, Pages = { 141-152 }, Year = { 1986 } } @Article{ Wol88, Author = { J.G. Wolfson }, Title = { {G}romov's compactness of pseudo-holomorphic curves and symplectic geometry }, Journal = { J. Differential Geom. }, Volume = { 28 }, Pages = { 283-405 }, Year = { 1988 } } @Incollection{ Wol88A, Author = { J.G. Wolfson }, Title = { {H}armonic sequences, harmonic maps and algebraic geometry }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 232-245 }, Year = { 1988 } } @Article{ Wol88B, Author = { J.G. Wolfson }, Title = { {H}armonic sequences and harmonic maps of surfaces into complex {G}rassmann manifolds }, Journal = { J. Differential Geom. }, Volume = { 27 }, Pages = { 161-178 }, Year = { 1988 } } @Article{ Wol89A, Author = { J.G. Wolfson }, Title = { {M}inimal surfaces in {K}\"ahler surfaces and {R}icci curvature }, Journal = { J. Differential Geom. }, Volume = { 29 }, Pages = { 281-294 }, Year = { 1989 } } @Unpublished{ WolA, Author = { S. Wolpert }, Title = { {O}n the variational theory of the {L}aplacian for hyperbolic surfaces }, Note = { preprint } } @Article{ Wol75, Author = { S. Wolpert }, Title = { {N}on-completeness of the {W}eil--{P}etersson metric for {T}eichm\"uller space }, Journal = { Pacific J. Math. }, Volume = { 61 }, Pages = { 573-577 }, Year = { 1975 } } @Article{ Wol82A, Author = { S. Wolpert }, Title = { {T}he {F}enchel-{N}ielsen deformation }, Journal = { Ann.\ of Math. }, Volume = { 115 }, Pages = { 501-528 }, Year = { 1982 } } @Article{ Wol85B, Author = { S. Wolpert }, Title = { {O}n the {W}eil--{P}etersson geometry of the moduli space of curves }, Journal = { Amer.\ J. Math. }, Volume = { 107 }, Pages = { 969-997 }, Year = { 1985 } } @Article{ Wol86B, Author = { S. Wolpert }, Title = { {C}hern forms and the {R}iemann tensor for the moduli space of curves }, Journal = { Invent.\ Math. }, Volume = { 85 }, Pages = { 119-145 }, Year = { 1986 } } @Article{ Wol87, Author = { S. Wolpert }, Title = { {G}eodesic length functions and the {N}ielsen problem }, Journal = { J. Differential Geom. }, Volume = { 25 }, Pages = { 275-296 }, Year = { 1987 } } @Article{ Won87, Author = { P.M. Wong }, Title = { {T}wistor spaces over {$6$}-dimensional {R}iemannian manifolds }, Journal = { Illinois J. Math. }, Volume = { 31 }, Pages = { 274-311 }, Year = { 1987 } } @Article{ Woo77, Author = { G. Woo }, Title = { {P}seudoparticle configuration in two-dimensional ferromagnets }, Journal = { J. Math.\ Phys. }, Volume = { 18 }, Pages = { 1264-1266 }, Year = { 1977 } } @Misc{ Woo, Author = { C.M. Wood }, Title = { {T}he amplitude of the {G}auss section } } @Unpublished{ WooA, Author = { C.M. Wood }, Title = { {A} class of harmonic almost product structures }, Note = { preprint } } @Misc{ WooB, Author = { C.M. Wood }, Title = { {H}armonic reduction of fibre bundles } } @Misc{ WooC, Author = { C.M. Wood }, Title = { {H}armonic sections, {E}instein's equation, and stress-energy } } @Misc{ WooD, Author = { C.M. Wood }, Title = { {H}armonic sections and equivariant harmonic maps } } @Misc{ WooE, Author = { C.M. Wood }, Title = { {H}armonic sections and gauge theory } } @Unpublished{ WooF, Author = { C.M. Wood }, Title = { {H}armonic symmetry breaking }, Note = { preprint } } @Misc{ WooG, Author = { C.M. Wood }, Title = { {O}n the energy of a unit vector field } } @Unpublished{ Woo83, Author = { C.M. Wood }, Title = { {S}ome energy-related functionals and their vertical variational theory }, Note = { Warwick Ph.D Thesis }, Year = { 1983 } } @Article{ Woo86, Author = { C.M. Wood }, Title = { {T}he {G}auss section of a {R}iemannian immersion }, Journal = { J. London Math.\ Soc. }, Volume = { 33 }, Pages = { 157-168 }, Year = { 1986 } } @Article{ Woo87, Author = { C.M. Wood }, Title = { {H}armonic sections and {Y}ang--{M}ills fields }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 54 }, Pages = { 544-558 }, Year = { 1987 } } @Incollection{ Woo88, Author = { C.M. Wood }, Title = { {H}armonic sections, {Y}ang--{M}ills fields and {E}instein's equation }, Booktitle = { {F}ibre bundles: their use in physics }, Publisher = { World Sci.\ Press }, Address = { Singapore }, Pages = { 160-170 }, Year = { 1988 } } @Incollection{ Woo89, Author = { C.M. Wood }, Title = { {${H}$}-structures and curvatures }, Booktitle = { {P}roc. {W}orkshop on {C}urvature {G}eometry {U}. {L}ancaster }, Pages = { 151-164 }, Year = { 1989 } } @Article{ Woo90, Author = { C.M. Wood }, Title = { {A}n existence theorem for harmonic sections }, Journal = { Manuscripta Math. }, Volume = { 68 }, Pages = { 69-75 }, Year = { 1990 } } @Article{ Woo93, Author = { C.M. Wood }, Title = { {I}nstability of the nearly {K}\"ahler six-sphere }, Journal = { J. Reine Angew.\ Math. }, Volume = { 439 }, Pages = { 205-212 }, Year = { 1993 } } @Article{ Woo95, Author = { C.M. Wood }, Title = { {H}armonic almost-complex structures }, Journal = { Compositio Math. }, Volume = { 99 }, Pages = { 183-212 }, Year = { 1995 } } @Incollection{ WooH, Author = { J.C. Wood }, Title = { {H}armonic maps and harmonic morphisms }, Booktitle = { {P}roc. {L}obachevsky {S}eminar }, Publisher = { World Sci. }, Address = { Singapore }, Note = { (to appear) } } @Unpublished{ Woo74, Author = { J.C. Wood }, Title = { {H}armonic mappings between surfaces }, Note = { Warwick Ph.D Thesis }, Year = { 1974 } } @Incollection{ Woo76, Author = { J.C. Wood }, Title = { {H}armonic maps and complex analysis }, Booktitle = { {C}omplex {A}nalysis and its {A}pplications, {V}ol. {I}{I}{I} }, Publisher = { ICTP }, Address = { Trieste }, Pages = { 289-308 }, Year = { 1976 } } @Article{ Woo77A, Author = { J.C. Wood }, Title = { {S}ingularities of harmonic maps and applications of the {G}auss--{B}onnet formula }, Journal = { Amer.\ J. Math. }, Volume = { 99 }, Pages = { 1329-1344 }, Year = { 1977 } } @Article{ Woo78, Author = { J.C. Wood }, Title = { {A} note on the fundamental group of a manifold of negative curvature }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 83 }, Pages = { 415-417 }, Year = { 1978 } } @Article{ Woo79, Author = { J.C. Wood }, Title = { {H}olomorphicity of certain harmonic maps from a surface to complex projective {$n$}-space }, Journal = { J. London Math.\ Soc. }, Volume = { 20 }, Pages = { 137-142 }, Year = { 1979 } } @Article{ Woo80, Author = { J.C. Wood }, Title = { {A}n extension theorem for holomorphic mappings }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 88 }, Pages = { 125-127 }, Year = { 1980 } } @Unpublished{ Woo81, Author = { J.C. Wood }, Title = { {C}onformality and holomorphicity of certain harmonic maps }, Note = { Leeds preprint }, Year = { 1981 } } @Unpublished{ Woo81A, Author = { J.C. Wood }, Title = { {N}on existence of solutions to certain {D}irichlet problems for harmonic maps {I} }, Note = { Preprint, University of Leeds }, Year = { 1981 } } @Incollection{ Woo81B, Author = { J.C. Wood }, Title = { {O}n the holomorphicity of harmonic maps from a surface }, Booktitle = { {G}lobal {D}ifferential {G}eometry and {G}lobal {A}nalysis }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 838 }, Pages = { 239-242 }, Series = { Lecture Notes in Math. }, Year = { 1981 } } @Article{ Woo83A, Author = { J.C. Wood }, Title = { {A}n extension theorem for holomorphic mappings (correction) }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 94 }, Pages = { 189 }, Year = { 1983 } } @Incollection{ Woo83B, Author = { J.C. Wood }, Title = { {S}ome aspects of harmonic maps from a surface to complex projective space }, Booktitle = { {D}ifferential {G}eometry and {M}athematical {P}hysics }, Editor = { M. Cahen and M. de~Wilde and L. Lemaire and L. Vanhecke }, Publisher = { Reidel }, Address = { Dortrecht, Boston, London }, Volume = { 3 }, Pages = { 177-186 }, Series = { Math.\ Phys.\ Stud. }, Year = { 1983 } } @Incollection{ Woo84, Author = { J.C. Wood }, Title = { {H}olomorphic differentials and classification theorems for harmonic maps and minimal immersions }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 168-175 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Incollection{ Woo85, Author = { J.C. Wood }, Title = { {O}n the {G}auss map of a harmonic morphism }, Booktitle = { {D}ifferential {G}eometry }, Editor = { L.A. Cordero }, Publisher = { Pitman }, Address = { Boston, London, Melbourne }, Volume = { 131 }, Pages = { 149-155 }, Series = { Pitman Res.\ Notes Math.\ Ser. }, Year = { 1985 } } @Incollection{ Woo86A, Author = { J.C. Wood }, Title = { {H}armonic morphisms, foliations and {G}auss maps }, Booktitle = { {C}omplex differential geometry and nonlinear partial differential equations }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 49 }, Pages = { 145-184 }, Series = { Contemp.\ Math. }, Year = { 1986 } } @Incollection{ Woo87A, Author = { J.C. Wood }, Title = { {T}wistor constructions for harmonic maps }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations }, Editor = { C.H. Gu and M. Berger and R. Bryant }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1255 }, Pages = { 130-159 }, Series = { Lecture Notes in Math. }, Year = { 1987 } } @Article{ Woo88A, Author = { J.C. Wood }, Title = { {T}he explicit construction and parametrization of all harmonic maps from the two-sphere to a complex {G}rassmannian }, Journal = { J. Reine Angew.\ Math. }, Volume = { 386 }, Pages = { 1-31 }, Year = { 1988 } } @Incollection{ Woo88B, Author = { J.C. Wood }, Title = { {O}n the explicit construction and parametrization of all harmonic maps from the two-sphere to a complex {G}rassmannian }, Booktitle = { {H}armonic mappings, twistors and {$\sigma$}-models }, Editor = { P. Gauduchon }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 246-260 }, Year = { 1988 } } @Article{ Woo89A, Author = { J.C. Wood }, Title = { {E}xplicit construction and parametrization of harmonic two-spheres in the unitary group }, Journal = { Proc.\ London Math.\ Soc. }, Volume = { 58 }, Pages = { 608-624 }, Year = { 1989 } } @Incollection{ Woo90A, Author = { J.C. Wood }, Title = { {H}armonic morphisms, conformal foliations and {S}eifert fibre spaces }, Booktitle = { {G}eometry of {L}ow-{D}imensional {M}anifolds, 1 }, Editor = { S.K. Donaldson and C.B. Thomas }, Publisher = { C.U.P. }, Address = { Cambridge }, Volume = { 150 }, Pages = { 247-259 }, Series = { London Math.\ Soc.\ Lecture Note Ser. }, Year = { 1990 } } @Article{ Woo91, Author = { J.C. Wood }, Title = { {L}ewy's theorem fails in higher dimensions }, Journal = { Math.\ Scand. }, Volume = { 69 }, Pages = { 166 }, Year = { 1991 } } @Article{ Woo92, Author = { J.C. Wood }, Title = { {H}armonic morphisms and {H}ermitian structures on {E}instein {$4$}-manifolds }, Journal = { Internat.\ J. Math. }, Volume = { 3 }, Pages = { 415-439 }, Year = { 1992 } } @Incollection{ Woo93A, Author = { J.C. Wood }, Title = { {H}armonic morphisms between {R}iemannian manifolds }, Booktitle = { {G}eometry and {G}lobal {A}nalysis }, Editor = { T. Kotake and S. Nishikawa and R. Schoen }, Publisher = { T\^ohoku Univ. }, Address = { Sendai }, Pages = { 413-422 }, Year = { 1993 } } @Incollection{ Woo94, Author = { J.C. Wood }, Title = { {H}armonic maps into symmetric spaces and integrable systems }, Booktitle = { {H}armonic maps and integrable systems }, Editor = { A.P. Fordy and J.C. Wood }, Publisher = { Vieweg }, Address = { Braunschweig, Wiesbaden }, Volume = { 23 }, Pages = { 29-55 }, Series = { Aspects of Math. }, Year = { 1994 } } @Unpublished{ WooI, Author = { R. Wood }, Title = { {A} note on harmonic polynomial maps }, Note = { preprint } } @Article{ Woo68, Author = { R. Wood }, Title = { {P}olynomial maps from spheres to spheres }, Journal = { Invent.\ Math. }, Volume = { 5 }, Pages = { 163-168 }, Year = { 1968 } } @Article{ Wu90, Author = { C.X. Wu }, Title = { {T}heorems on nonexistence of stable harmonic maps }, Journal = { Adv.\ in Math.\ (Beijing) }, Volume = { 19 }, Pages = { 462-466 }, Year = { 1990 } } @Article{ Wu91, Author = { C.X. Wu }, Title = { {S}ome results on stable harmonic maps }, Journal = { Acta Math.\ Sinica }, Volume = { 34 }, Pages = { 27-32 }, Note = { (Chinese) }, Year = { 1991 } } @Article{ Wu97, Author = { D. Wu }, Title = { {H}armonic diffeomorphisms between complete surfaces }, Journal = { Anal.\ Global Anal.\ Geom. }, Volume = { 15 }, Pages = { 133--139 }, Year = { 1997 } } @Incollection{ Wu93, Author = { H. Wu }, Title = { {B}anach manifolds of minimal surfaces in the {$4$}-sphere }, Booktitle = { {D}ifferential {G}eometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence RI }, Volume = { 54 }, Pages = { 513-539 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Unpublished{ Wu95, Author = { H. Wu }, Title = { {A} simple way for determining the normalized potentials for harmonic maps }, Note = { Preprint }, Year = { 1995 } } @Unpublished{ Wu96, Author = { H. Wu }, Title = { {D}enseness of plain constant mean curvature surfaces }, Note = { Preprint }, Year = { 1996 } } @Unpublished{ Wu96A, Author = { H. Wu }, Title = { {O}n the dressing action of loop groups on constant mean curvature surfaces }, Note = { Preprint }, Year = { 1996 } } @Misc{ Wu, Author = { H.H. Wu }, Title = { {O}ld and now invariant metrics on complex manifolds } } @Misc{ WuA, Author = { H.H. Wu }, Title = { {S}ubharmonic functions and the volume of a noncompact manifold } } @Article{ Wu67, Author = { H.H. Wu }, Title = { {N}ormal families of holomorphic mappings }, Journal = { Acta Math. }, Volume = { 119 }, Pages = { 193-233 }, Year = { 1967 } } @Incollection{ Wu68, Author = { H.H. Wu }, Title = { {M}appings of {R}iemann surfaces ({N}evanlinna theory) }, Booktitle = { {E}ntire {F}unctions and related parts of {A}nalysis }, Editor = { S.S. Chern and L. Ehrenpreis and J. Korevaar and W.H.J. Fuchs and L.A. Rubel }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, R.I. }, Volume = { 11 }, Pages = { 480-532 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1968 } } @Book{ Wu70, Author = { H.H. Wu }, Title = { {T}he equidistribution theory of holomorphic curves }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 64 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1970 } } @Incollection{ Wu82, Author = { H.H. Wu }, Title = { {T}he {B}ochner technique }, Booktitle = { {D}{D}1 (1980) }, Publisher = { Sci.\ Press. }, Address = { Beijing }, Pages = { 929-1071 }, Year = { 1982 } } @Book{ Wu87, Author = { H.H. Wu }, Title = { {T}he {B}ochner technique in differential geometry }, Publisher = { Horwood Acad.\ Publ. }, Series = { Math.\ Rep. }, Year = { 1987 } } @Article{ Xan81, Author = { B.C. Xanthopoulos }, Title = { {H}armonic maps and self-dual {${S}{U}(3)$}-gauge field }, Journal = { J. Phys.\ A }, Volume = { 14 }, Pages = { 1445-1455 }, Year = { 1981 } } @Article{ Xan84, Author = { B.C. Xanthopoulos }, Title = { {A} geometric notion of complete integrability }, Journal = { Phys.\ Lett.\ A }, Volume = { 105 }, Pages = { 335-338 }, Year = { 1984 } } @Article{ Xav81, Author = { F. Xavier }, Title = { {T}he {G}auss map of complete non-flat minimal surfaces cannot omit {$7$} points of the sphere }, Journal = { Ann.\ of Math. }, Volume = { 113 }, Pages = { 211-214 }, Year = { 1981 } } @Article{ Xav93, Author = { F. Xavier }, Title = { {O}n the structure of complete simply connected embedded minimal surfaces }, Journal = { J. Geom.\ Anal. }, Volume = { 3 }, Pages = { 513-527 }, Year = { 1993 } } @Article{ Xia91, Author = { C.Y. Xia }, Title = { {A} pinching theorem for minimal submanifolds in a sphere }, Journal = { Arch.\ Math.\ (Basel) }, Volume = { 57 }, Pages = { 307-312 }, Year = { 1991 } } @Unpublished{ Xia, Author = { L. Xiao }, Title = { {O}n homogeneity of some types of isoparametric submanifolds in spheres }, Note = { preprint } } @Unpublished{ Xin, Author = { Y.L. Xin }, Title = { {S}ome {L}iouville-type theorems for harmonic and holomorphic maps }, Note = { preprint } } @Article{ Xin80, Author = { Y.L. Xin }, Title = { {S}ome results on stable harmonic maps }, Journal = { Duke Math.\ J. }, Volume = { 47 }, Pages = { 609-613 }, Year = { 1980 } } @Article{ Xin81, Author = { Y.L. Xin }, Title = { {T}opology of certain submanifolds in the {E}uclidean sphere }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 82 }, Pages = { 643-648 }, Year = { 1981 } } @Incollection{ Xin82, Author = { Y.L. Xin }, Title = { {O}n stable harmonic maps and their application }, Booktitle = { {P}roc. {B}eijing {S}ymposium on {D}ifferential {G}eometry and {D}ifferential {E}quations, {V}ol. 3 }, Publisher = { Gordon and Breach }, Pages = { 1611-1619 }, Year = { 1982 } } @Article{ Xin82A, Author = { Y.L. Xin }, Title = { {A} remark on harmonic maps }, Journal = { Chinese Ann.\ Math. }, Volume = { 3 }, Pages = { 13-17 }, Year = { 1982 } } @Article{ Xin82B, Author = { Y.L. Xin }, Title = { {S}ome existence theorems for harmonic maps in {R}iemannian manifolds }, Journal = { Sci.\ Sinica Ser.\ A }, Volume = { 25 }, Pages = { 1271-1278 }, Year = { 1982 } } @Article{ Xin84, Author = { Y.L. Xin }, Title = { {A}n application of integral currents to the vanishing theorems }, Journal = { Sci.\ Sinica }, Volume = { 27 }, Pages = { 233-241 }, Year = { 1984 } } @Incollection{ Xin84A, Author = { Y.L. Xin }, Title = { {N}on-existence and existence for harmonic maps in {R}iemannian manifolds }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations, {S}hanghai--{H}efei, 1981 }, Publisher = { Sci.\ Press }, Address = { Beijing }, Pages = { 529-538 }, Year = { 1984 } } @Article{ Xin84B, Author = { Y.L. Xin }, Title = { {R}emarks on gap phenomena for {Y}ang--{M}ills fields }, Journal = { Sci.\ Sinica }, Volume = { 27 }, Pages = { 936-942 }, Year = { 1984 } } @Article{ Xin84C, Author = { Y.L. Xin }, Title = { {S}ome properties for stress energy tensor of smooth map }, Journal = { Kexue Tongbao (English Ed.) }, Volume = { 29 }, Pages = { 1004-1007 }, Year = { 1984 } } @Article{ Xin85, Author = { Y.L. Xin }, Title = { {A}n estimate for the image diameter and its application to submanivolds with parallel mean curvature }, Journal = { Acta Math.\ Sci. }, Volume = { 5 }, Pages = { 303-308 }, Year = { 1985 } } @Article{ Xin85A, Author = { Y.L. Xin }, Title = { {H}olomorphicity of a class of harmonic maps }, Journal = { Acta Math.\ Sinica }, Volume = { 28 }, Pages = { 382-386 }, Year = { 1985 } } @Article{ Xin86, Author = { Y.L. Xin }, Title = { {D}ifferential forms, conservation law and monotonicity formula }, Journal = { Sci.\ Sinica }, Volume = { 29 }, Pages = { 40-50 }, Year = { 1986 } } @Incollection{ Xin87, Author = { Y.L. Xin }, Title = { {L}iouville type theorems and regularity of harmonic maps }, Booktitle = { {D}ifferential {G}eometry and {D}ifferential {E}quations }, Editor = { C.H. Gu and M. Berger and R. Bryant }, Publisher = { Springer }, Address = { Berlin }, Volume = { 1255 }, Pages = { 199-208 }, Series = { Lecture Notes in Math. }, Year = { 1987 } } @Article{ Xin89, Author = { Y.L. Xin }, Title = { {C}ones and conelike harmonic maps }, Journal = { J. Math.\ (Wuhan) }, Volume = { 91 }, Pages = { 87-92 }, Note = { (Chinese, English summary) }, Year = { 1989 } } @Incollection{ Xin89A, Author = { Y.L. Xin }, Title = { {R}egularity of harmonic maps into certain homogeneous spaces }, Booktitle = { {D}ifferential {G}eometry and {T}opology }, Editor = { B. Jiang and C.K. Peng and Z. Hou }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 1369 }, Pages = { 295-305 }, Series = { Lecture Notes in Math. }, Year = { 1989 } } @Article{ Xin89B, Author = { Y.L. Xin }, Title = { {S}table harmonic maps from complete manifolds }, Journal = { Acta Math.\ Sci. }, Volume = { 9 }, Pages = { 415-420 }, Year = { 1989 } } @Article{ Xin89C, Author = { Y.L. Xin }, Title = { {T}he theorems of {B}ernstein type of a minimal surface in {${\bf {R}}^3$} and the value distribution of its {G}auss map }, Journal = { Adv.\ in Math. }, Volume = { 18 }, Year = { 1989 } } @Article{ Xin91, Author = { Y.L. Xin }, Title = { {O}n the {G}auss image of a spacelike hypersurface with constant mean curvature in {M}inkowski space }, Journal = { Comment.\ Math.\ Helv. }, Volume = { 66 }, Pages = { 590-598 }, Year = { 1991 } } @Article{ Xin92, Author = { Y.L. Xin }, Title = { {R}egularity of harmonic maps into positively curved manifolds }, Journal = { Chinese Ann.\ Math. }, Volume = { 1314 }, Pages = { 385-395 }, Year = { 1992 } } @Article{ Xin93, Author = { Y.L. Xin }, Title = { {E}quivariant harmonic maps into the sphere via isoparametric maps }, Journal = { Manuscripta Math. }, Volume = { 79 }, Pages = { 49-71 }, Year = { 1993 } } @Incollection{ Xin93A, Author = { Y.L. Xin }, Title = { {R}iemannian submersions and equivariant harmonic maps }, Booktitle = { {P}roceedings of a conference on differential geometry in honor of {P}rofessor {S}u {B}uchin }, Publisher = { World Scientific }, Address = { Singapore }, Pages = { 272-287 }, Year = { 1993 } } @Article{ Xin94, Author = { Y.L. Xin }, Title = { {O}n harmonic representative of {$\pi_{2m+1}({S}^{2m+1})$} }, Journal = { Math.\ Z. }, Volume = { 216 }, Pages = { 389-400 }, Year = { 1994 } } @Article{ Xin95, Author = { Y.L. Xin }, Title = { {H}armonic maps of bounded symmetric domains }, Journal = { Math.\ Ann. }, Volume = { 303 }, Pages = { 417-433 }, Year = { 1995 } } @Article{ Xin96, Author = { Y.L. Xin }, Title = { {H}eat flow of equivariant harmonic maps from {${B}^3$} into {${\bf {C}}{P}^2$} }, Journal = { Pacific J. Math. }, Volume = { 176 }, Pages = { 563--579 }, Year = { 1996 } } @Article{ XinYan95, Author = { Y.L. Xin and Y.H. Yang }, Title = { {R}egularity of {$p$}-harmonic maps into certain manifolds with positive sectional curvature }, Journal = { J. Reine Angew.\ Math. }, Volume = { 466 }, Pages = { 1-17 }, Year = { 1995 } } @Article{ XuYan93, Author = { X.W. Xu and P.C. Yang }, Title = { {A} construction of {$m$}-harmonic maps of spheres }, Journal = { Internat.\ J. Math. }, Volume = { 4 }, Pages = { 521-533 }, Year = { 1993 } } @Article{ Yam87, Author = { K. Yamada }, Title = { {M}inimal tori in {${S}^3$} whose lines of curvature lie in {${S}^2$} }, Journal = { Tokyo J. Math. }, Volume = { 10 }, Pages = { 215-226 }, Year = { 1987 } } @Unpublished{ Yan, Author = { K. Yang }, Title = { {H}olomorphic curves in the complex hyperquadric }, Note = { preprint } } @Book{ Yan87, Author = { K. Yang }, Title = { {A}lmost complex homogeneous spaces and their submanifolds }, Publisher = { World Sci.\ Publ. }, Address = { Singapore }, Year = { 1987 } } @Article{ Yan88, Author = { K. Yang }, Title = { {H}orizontal holomorphic curves in {${S}p(n)$}-flag manifolds }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 103 }, Pages = { 265-273 }, Year = { 1988 } } @Book{ Yan89, Author = { K. Yang }, Title = { {C}omplete and compact minimal surfaces }, Publisher = { Kluwer Acad.\ Publ. }, Address = { Dordrecht }, Volume = { 54 }, Series = { Math.\ Appl. }, Year = { 1989 } } @Article{ Yan89A, Author = { K. Yang }, Title = { {M}eromorphic functions on a compact {R}iemann surface and associated complete mimimal surfacs }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 105 }, Pages = { 706-711 }, Year = { 1989 } } @Article{ Yan89B, Author = { K. Yang }, Title = { {P}l{\"u}cker formulae for the orthogonal group }, Journal = { Bull.\ Austral.\ Math.\ Soc. }, Volume = { 40 }, Pages = { 447-456 }, Year = { 1989 } } @Article{ Yan91, Author = { K. Yang }, Title = { {M}inimal immersions of punctured compact {R}iemann surfaces in {${\bf {R}}^3$} }, Journal = { Proc.\ Amer.\ Math.\ Soc. }, Volume = { 113 }, Pages = { 809-816 }, Year = { 1991 } } @Article{ YanYau80, Author = { P. Yang and S.T. Yau }, Title = { {E}igenvalues of the {L}aplacian of compact {R}iemann surfaces and minimal submanifolds }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 7 }, Pages = { 55-63 }, Year = { 1980 } } @Article{ Yan87A, Author = { W.M. Yang }, Title = { {O}n affine minimal rotation surfaces and conoid in{${A}^3$} }, Journal = { J. Math.\ (Wuhan) }, Volume = { 7 }, Pages = { 205-210 }, Year = { 1987 } } @Article{ Yan93, Author = { X. Yang }, Title = { {T}he existence of harmonic maps from and annulus to {${S}^2$} with symmetric boundary value }, Journal = { Acta Math.\ Sinica }, Volume = { 9 }, Pages = { 401-405 }, Year = { 1993 } } @Article{ Yan92, Author = { X.F. Yang }, Title = { {O}n the equivariant harmonic maps between surfaces in {${\bf {R}}^3$} }, Journal = { Systems Sci.\ Math.\ Sci. }, Volume = { 5 }, Pages = { 205-212 }, Year = { 1992 } } @Article{ Yan93A, Author = { X.F. Yang }, Title = { {T}he existence of harmonic maps from an annulus to {${S}^2$} with symmetric boundary value }, Journal = { Acta Math.\ Sinica }, Volume = { 9 }, Pages = { 401-405 }, Year = { 1993 } } @Article{ Yan97, Author = { Y.H. Yang }, Title = { {F}atou property of harmonic maps from complete manifolds with simple type ends }, Journal = { Hokkaido Math.\ J. }, Volume = { 26 }, Pages = { 101--114 }, Year = { 1997 } } @Article{ Yas87, Author = { T. Yasuoka }, Title = { {T}he {D}irichlet problem at infinity and complex analysis on {H}adamard manifolds }, Journal = { Nagoya Math.\ J. }, Volume = { 106 }, Pages = { 79-90 }, Year = { 1987 } } @Article{ Yau71, Author = { S.T. Yau }, Title = { {O}n the fundamental group of compact manifolds of non-positive curvature }, Journal = { Ann.\ of Math. }, Volume = { 93 }, Pages = { 579-585 }, Year = { 1971 } } @Article{ Yau74, Author = { S.T. Yau }, Title = { {N}onexistence of continuous convex functions on certain {R}iemannian manifolds }, Journal = { Math.\ Ann. }, Volume = { 207 }, Pages = { 269-270 }, Year = { 1974 } } @Article{ Yau74A, Author = { S.T. Yau }, Title = { {S}ubmanifolds with constant mean curvature. {I} }, Journal = { Amer.\ J. Math. }, Volume = { 96 }, Pages = { 346-366 }, Year = { 1974 } } @Article{ Yau74B, Author = { S.T. Yau }, Title = { {S}ubmanifolds with constant mean curvature {I} }, Journal = { Amer.\ J. Math. }, Volume = { 96 }, Pages = { 346-366 }, Year = { 1974 } } @Article{ Yau75, Author = { S.T. Yau }, Title = { {H}armonic functions on complete {R}iemannian manifolds }, Journal = { Comm.\ Pure Appl.\ Math. }, Volume = { 28 }, Pages = { 201-228 }, Year = { 1975 } } @Article{ Yau75A, Author = { S.T. Yau }, Title = { {S}ubmanifolds with constant mean curvature. {I}{I} }, Journal = { Amer.\ J. Math. }, Volume = { 97 }, Pages = { 76-100 }, Year = { 1975 } } @Article{ Yau76, Author = { S.T. Yau }, Title = { {S}ome function-theoretic properties of complete {R}iemannian manifolds and their applications to geometry }, Journal = { Indiana Univ.\ Math.\ J. }, Volume = { 25 }, Pages = { 659-670 }, Year = { 1976 } } @Article{ Yau78, Author = { S.T. Yau }, Title = { {A} general {S}chwarz lemma for {K}\"ahler manifolds }, Journal = { Amer.\ J. Math. }, Volume = { 100 }, Pages = { 197-203 }, Year = { 1978 } } @Incollection{ Yau79, Author = { S.T. Yau }, Title = { {H}armonic maps between {R}iemannian manifolds }, Booktitle = { {C}onference {P}ark {C}ity, {U}tah }, Publisher = { M. Dekker }, Address = { New York }, Volume = { 48 }, Pages = { 307-311 }, Series = { Lecture Notes in Pure and Appl.\ Math. }, Year = { 1979 } } @Incollection{ Yau82, Author = { S.T. Yau }, Title = { {S}urvey on partial differential equations in differential geometry }, Booktitle = { {S}eminar on {D}ifferential {G}eometry }, Editor = { S.T. Yau }, Publisher = { Princeton Univ.\ Press }, Address = { Princeton }, Volume = { 102 }, Pages = { 3-71 }, Series = { Ann.\ of Math.\ Stud. }, Year = { 1982 } } @Incollection{ Yau84, Author = { S.T. Yau }, Title = { {M}inimal surfaces and their r\^ole in differential geometry }, Booktitle = { {G}lobal {R}iemannian {G}eometry }, Editor = { T.J. Willmore and N.J. Hitchin }, Publisher = { E. Horwood }, Address = { Chichester }, Pages = { 99-103 }, Series = { Ellis Horwood Ser.\ Math.\ Appl. }, Year = { 1984 } } @Incollection{ Yau84A, Author = { S.T. Yau }, Title = { {A} survey on {K}\"ahler--{E}insein metrics }, Booktitle = { {C}omplex {A}nalysis of {S}everal {V}ariables }, Editor = { Y.T. Siu }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence, RI }, Volume = { 41 }, Pages = { 285-289 }, Series = { Proc.\ Sympos.\ Pure Math. }, Year = { 1984 } } @Unpublished{ Yau86, Author = { S.T. Yau }, Title = { {N}onlinear analysis }, Note = { Colloq. Lecture Amer. Math. Soc. }, Year = { 1986 } } @Article{ Yau87, Author = { S.T. Yau }, Title = { {N}onlinear analysis in geometry }, Journal = { Enseign.\ Math. }, Volume = { 33 }, Pages = { 109-158 }, Year = { 1987 } } @Article{ Ye92, Author = { D. Ye }, Title = { {A}nalyse asymptotique des applications harmoniques minimisantes sur un domaine compris entre deux cercles vers une vari{\'e}t{\'e} riemannienne }, Journal = { C. R. Acad.\ Sci.\ Paris }, Volume = { 315 }, Pages = { 979-982 }, Year = { 1992 } } @Article{ Ye95, Author = { D. Ye }, Title = { {S}ur la multiplicit{\'e} des applications harmoniques minimisantes {\`a} valeurs dans {${S}^1$} }, Journal = { C. R. Acad.\ Sci.\ Paris S\'er.\ I Math. }, Volume = { 320 }, Pages = { 1107-1112 }, Year = { 1995 } } @Article{ YeZho94, Author = { D. Ye and F. Zhou }, Title = { {M}inimizing harmonic mappings into a circle }, Journal = { Houston J. Math. }, Volume = { 20 }, Pages = { 475-490 }, Year = { 1994 } } @Misc{ Ye, Author = { R. Ye }, Title = { {H}ow to blow infinitely large soap bubbles with a fixed boundary } } @Unpublished{ Ye84, Author = { R. Ye }, Title = { {R}anderegularit\"at von {M}inimalfl\"achen }, Note = { Diplomarbeit Bonn }, Year = { 1984 } } @Unpublished{ Ye86, Author = { R. Ye }, Title = { {R}egularity of a minimal surface at its free boundary }, Note = { Preprint, SFB72 Bonn }, Year = { 1986 } } @Article{ Ye87, Author = { R. Ye }, Title = { {A} priori estimates for minimal surfaces with free boundary, which are not minima of the area }, Journal = { Manuscripta Math. }, Volume = { 58 }, Pages = { 95-107 }, Year = { 1987 } } @Unpublished{ Ye87A, Author = { R. Ye }, Title = { {U}ber die {E}xistenz, {R}egularit\"at und {E}ndlichkeit von {M}inimalfl\"achen mit freiem {R}and }, Note = { Bonn preprint }, Year = { 1987 } } @Unpublished{ Ye88, Author = { R. Ye }, Title = { {A} new approach to embedded minimal surfaces }, Note = { Preprint, SFB256 Bonn }, Year = { 1988 } } @Article{ Ye91, Author = { R. Ye }, Title = { {O}n the existence of area-minimizing surfaces with free boundary }, Journal = { Math.\ Z. }, Volume = { 206 }, Pages = { 321-331 }, Year = { 1991 } } @Misc{ Yiu, Author = { P. Yiu }, Title = { {C}omposition of sums of squares formulae with integer coefficients } } @Misc{ YiuA, Author = { P. Yiu }, Title = { {Q}uadratic forms between {E}uclidean spheres } } @Article{ Yiu86, Author = { P. Yiu }, Title = { {Q}uadratic forms between spheres and the non-existence of sums of squares formulae }, Journal = { Math.\ Proc.\ Cambridge Philos.\ Soc. }, Volume = { 100 }, Pages = { 493-504 }, Year = { 1986 } } @Incollection{ Yoo91, Author = { J.H. Yoon }, Title = { {G}eometric origin of {${\bf {C}}{P}^{{N}-1}$} sigma models }, Booktitle = { {P}roc. {F}ourth {A}sia {P}acific {P}hysics {C}onf. {V}ol 1,2 ({S}eoul 1990) }, Publisher = { World Scientific }, Address = { Singpore }, Pages = { 225-228 }, Year = { 1991 } } @Article{ Yor72, Author = { S. Yorozu }, Title = { {N}otes on harmonic transformations }, Journal = { T\^ohoku Math.\ J. }, Volume = { 24 }, Pages = { 441-447 }, Year = { 1972 } } @Article{ Yu81, Author = { Q.H. Yu }, Title = { {H}armonic mappings and totally geodesic mappings }, Journal = { Kexue Tongbao (Chinese) }, Volume = { 26 }, Pages = { 1414-1417 }, Year = { 1981 } } @Article{ Yu82, Author = { Q.H. Yu }, Title = { {H}armonic mapping and totally geodesic mapping }, Journal = { Kexue Tongbao (English Ed.) }, Volume = { 27 }, Pages = { 482-486 }, Year = { 1982 } } @Article{ Yu85, Author = { Q.H. Yu }, Title = { {B}ounded harmonic maps }, Journal = { Acta Math.\ Sinica }, Volume = { 1 }, Pages = { 16-21 }, Year = { 1985 } } @Article{ Yuz81, Author = { S. Yuzvinsky }, Title = { {O}rthogonal pairings of {E}uclidean spaces }, Journal = { Michigan Math.\ J. }, Volume = { 28 }, Pages = { 131-145 }, Year = { 1981 } } @Incollection{ Zak82, Author = { W.J. Zakrzewski }, Title = { {C}lassical solutions to {${\bf {C}}{P}^{n-1}$} models and their generalizations, integrable quantum field theories }, Booktitle = { {I}ntegrable {Q}uantum {F}ield {T}heory }, Editor = { J. Hictarinta and C. Montonen }, Publisher = { Springer }, Address = { Berlin, Heidelberg, New York }, Volume = { 151 }, Pages = { 160-188 }, Series = { Lecture Notes in Phys. }, Year = { 1982 } } @Article{ Zak84, Author = { W.J. Zakrzewski }, Title = { {C}lassical solutions of two-dimensional {G}rassmannian models }, Journal = { J. Geom.\ Phys. }, Volume = { 1 }, Pages = { 39-63 }, Year = { 1984 } } @Article{ Zak85, Author = { W.J. Zakrzewski }, Title = { {$\sigma$}-models in even dimensional spaces }, Journal = { Nuclear Phys.\ B }, Volume = { 262 }, Pages = { 120-132 }, Year = { 1985 } } @Article{ Zak86, Author = { W.J. Zakrzewski }, Title = { {C}lassical solutions of some {${C}{P}^1$}-like models }, Journal = { Lett.\ Math.\ Phys. }, Volume = { 12 }, Pages = { 283-290 }, Year = { 1986 } } @Article{ Zak86A, Author = { W.J. Zakrzewski }, Title = { {S}ome {$\sigma$}-like models in even dimensional spaces }, Journal = { Acta Phys.\ Polon.\ B }, Volume = { 17 }, Pages = { 351-363 }, Year = { 1986 } } @Incollection{ Zak87, Author = { W.J. Zakrzewski }, Title = { {S}ome classical solutions of {${U}({N})$} chiral models }, Booktitle = { {W}orkshop on {S}kyrmions and {A}nomalies }, Publisher = { World Sci. }, Address = { Singapore }, Pages = { 475-487 }, Year = { 1987 } } @Book{ Zak89, Author = { W.J. Zakrzewski }, Title = { {L}ow-dimensional sigma modles }, Publisher = { Adam Hilger }, Address = { Bristol }, Year = { 1989 } } @Article{ Zak91, Author = { W.J. Zakrzewski }, Title = { {S}oliton-like scattering in the {${O}(3)$} {$\sigma$}-model in {$(2+1)$} dimensions }, Journal = { Nonlinearity }, Volume = { 4 }, Pages = { 429-475 }, Year = { 1991 } } @Article{ Zan88, Author = { A. Zandi }, Title = { {M}inimal immersions of surfaces in quaternionic projective spaces }, Journal = { Tsukuba J. Math. }, Volume = { 12 }, Pages = { 423-440 }, Year = { 1988 } } @Unpublished{ Zha, Author = { D. Zhang }, Title = { {O}n the existence of regular minimizing {$m$}-harmonic maps }, Note = { preprint } } @Misc{ ZhaA, Author = { D. Zhang }, Title = { {A}n uniqueness result of an exterior problem and a {L}iouville theorem for harmonic maps } } @Article{ Zha89, Author = { D. Zhang }, Title = { {T}he existence of nonminimal regular harmonic maps from {${B}^3$} to {${S}^2$} }, Journal = { Ann.\ Scuola Norm.\ Sup.\ Pisa Cl.\ Sci. }, Volume = { 16 }, Pages = { 355-365 }, Year = { 1989 } } @Unpublished{ Zha86, Author = { L.N. Zhang }, Title = { {H}armonic mapping actions and non-linear {$\sigma$}-model }, Note = { I.C.T.P. preprint }, Year = { 1986 } } @Misc{ ZhaB, Author = { X. Zhang }, Title = { {T}he heat flow and harmonic maps on a class of manifolds } } @Article{ Zha92, Author = { X.M. Zhang }, Title = { {I}sometric immersion of minimal spherical submanifold via the second standard immersion of the sphere }, Journal = { Tamkang J. Math. }, Volume = { 23 }, Pages = { 145-159 }, Year = { 1992 } } @Incollection{ Zhe93, Author = { S. Zheng }, Title = { {O}n the isolatedness of the solutions of {P}lateau's problem }, Booktitle = { {D}ifferential geometry }, Editor = { R.E. Greene and S.T. Yau }, Publisher = { Amer.\ Math.\ Soc. }, Address = { Providence R.I. }, Volume = { 54:1 }, Pages = { 541-560 }, Series = { Proc.\ Sympos.\ Pure Math }, Year = { 1993 } } @Article{ Zhe89, Author = { Y. Zheng }, Title = { {A} quantization of curvature of harmonic two-spheres in {G}rassmann manifolds }, Journal = { Trans.\ Amer.\ Math.\ Soc. }, Volume = { 316 }, Pages = { 193-214 }, Year = { 1989 } } @Incollection{ Zho84, Author = { J.Q. Zhong }, Title = { {T}he degree of strong nondegeneracy of the bisectional curvature of exceptional bounded symmetric domains }, Booktitle = { {S}everal {C}omplex {V}ariables ({H}angzhou 1981) }, Editor = { J.J. Kohn and Q.K. Lu and R. Remmert and Y.T. Siu }, Publisher = { Birkha\"user }, Address = { Boston }, Pages = { 127-140 }, Year = { 1984 } } @Incollection{ Zho93, Author = { Z.X. Zhou }, Title = { {C}onstruction of explicit solutions of modified principal chiral fields in {$1+2$} dimensions via {D}arboux transformations }, Booktitle = { {D}ifferential {G}eometry ({S}hanghai, 1991) }, Publisher = { World Sci.\ Publishing }, Address = { River Edge, NJ }, Pages = { 325-332 }, Year = { 1993 } } @Article{ Zou85, Author = { Y.M. Zou }, Title = { {M}inimal immersions of rank one compact symmetric spaces into spheres }, Journal = { Sci.\ Sinica Ser.\ A }, Volume = { 28 }, Pages = { 263-272 }, Year = { 1985 } } @Article{ Oks84, Author = { B. {\O}ksendal }, Title = { {F}inely harmonic morphisms, {B}rownian path preserving functions and conformal martingales }, Journal = { Invent.\ Math. }, Volume = { 75 }, Year = { 1984 } }