Matteo Novaga

Università di Pisa

Long-time behaviour of fractional mean curvature flow

I will consider the volume-constrained fractional mean curvature flow of a nearly spherical set, showing long-time existence and exponential convergence to a ball. The result applies in particular to convex initial data, under the assumption of global existence. In a similar way one can show the exponential convergence to a constant for the fractional mean curvature flow of a periodic Lipschitz graph.