English

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

Differential Geometry 2025-05-23 v2

Abstract

We prove that, in the flat torus and in any dimension, the volume-preserving mean curvature flow and the surface diffusion flow, starting C1,1C^{1,1}-close to a strictly stable critical set of the perimeter EE, exist for all times and converge to a translate of EE exponentially fast as time goes to infinity.

Keywords

Cite

@article{arxiv.2305.11100,
  title  = {Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus},
  author = {Daniele De Gennaro and Antonia Diana and Andrea Kubin and Anna Kubin},
  journal= {arXiv preprint arXiv:2305.11100},
  year   = {2025}
}