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.
Stability of the ball under volume preserving fractional mean curvature flow
Cesaroni A.;
2024
Abstract
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.
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