Calculus of Variations and Geometric Measure Theory

D. De Gennaro - A. Diana - A. Kubin - A. Kubin

Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus

created by kubin1 on 22 May 2023
modified by degennaro on 02 Apr 2024


Accepted Paper

Inserted: 22 may 2023
Last Updated: 2 apr 2024

Journal: Math. Ann.
Year: 2023

ArXiv: 2305.11100 PDF


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.