Accepted Paper

Inserted: 22 may 2023
Last Updated: 2 apr 2024

Journal: Math. Ann.
Year: 2023

Abstract:

We prove that, in the flat torus and in any dimension, the volume-preserving mean curvature flow and the surface diffusion flow, starting $C^{1,1}-$close to a strictly stable critical set of the perimeter $E$, exist for all times and converge to a translate of $E$ exponentially fast as time goes to infinity.