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arXiv · 2201.04174

Long Time Behaviour of the Discrete Volume Preserving Mean Curvature Flow in the Flat Torus

Daniele De Gennaro·Anna Kubin
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Abstract

We show that the discrete approximate volume preserving mean curvature flow in the flat torus $\mathbb{T}^N$ starting near a strictly stable critical set $E$ of the perimeter converges in the long time to a translate of $E$ exponentially fast. As an intermediate result we establish a new quantitative estimate of Alexandrov type for periodic strictly stable constant mean curvature hypersurfaces. Finally, in the two dimensional case a complete characterization of the long time behaviour of the discrete flow with arbitrary initial sets of finite perimeter is provided.

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Daniele De Gennaro, Anna Kubin. 2022-01-11. Long Time Behaviour of the Discrete Volume Preserving Mean Curvature Flow in the Flat Torus. https://arxiv.org/abs/2201.04174

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