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arXiv · 2305.11100

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

Daniele De Gennaro·Antonia Diana·Andrea Kubin·Anna Kubin
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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.

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Daniele De Gennaro, Antonia Diana, Andrea Kubin, Anna Kubin. 2023-05-18. Stability of the surface diffusion flow and volume-preserving mean curvature flow in the flat torus. https://doi.org/10.1007/s00208-024-02863-3

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