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

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.

References in corpus (5)

• Minimality via second variation for a nonlocal isoperimetric problem
• Surface diffusion flow near spheres
• On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow
• The surface diffusion flow with elasticity in the plane
• Asymptotic of the Discrete Volume-Preserving Fractional Mean Curvature Flow via a Nonlocal Quantitative Alexandrov Theorem