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

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2024年4月13日

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Daniele De Gennaro,
Antonia Diana,
Andrea Kubin,
Anna Kubin

摘要

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