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

De Gennaro, Danièle; Kubin, Anna (2022), Long Time Behaviour of the Discrete Volume Preserving Mean Curvature Flow in the Flat Torus. https://basepub.dauphine.psl.eu/handle/123456789/23266

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
37
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Author(s)
De Gennaro, Danièle
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kubin, Anna
Politecnico di Torino = Polytechnic of Turin [Polito]
Abstract (EN)
We show that the discrete approximate volume preserving mean curvature flow in the flat torus 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.
Subjects / Keywords
Geometric evolution equations; Minimizing movement