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

Abstract

AbstractWe prove that, in the flat torus and in any dimension, the volume-preserving mean curvature flow and the surface diffusion flow, starting $$C^{1,1}$$ 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.