Stability of the ball under volume preserving fractional mean curvature flow

Annalisa Cesaroni, Matteo Novaga

Published 2022-04-11Version 1

We consider the volume constrained fractional mean curvature flow of a nearly spherical set, and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data, under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.