Asymptotic of the Discrete Volume-Preserving Fractional Mean Curvature Flow via a Nonlocal Quantitative Alexandrov Theorem

De Gennaro, Danièle; Kubin, Andrea; Kubin, Anna

De Gennaro, Danièle; Kubin, Andrea; Kubin, Anna (2023), Asymptotic of the Discrete Volume-Preserving Fractional Mean Curvature Flow via a Nonlocal Quantitative Alexandrov Theorem, Nonlinear Analysis, 228, p. 27. 10.1016/j.na.2022.113200

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Type

Article accepté pour publication ou publié

Date

2023

Journal name

Nonlinear Analysis

Volume

228

Publisher

Elsevier

Published in

Paris

Publication identifier

10.1016/j.na.2022.113200

Metadata

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Author(s)

De Gennaro, Danièle
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Kubin, Andrea
Technische Universität München [TUM]
Kubin, Anna
Politecnico di Torino

Abstract (EN)

We characterize the long time behaviour of a discrete-in-time approximation of the volume preserving fractional mean curvature flow. In particular, we prove that the discrete flow starting from any bounded set of finite fractional perimeter converges exponentially fast to a single ball. As an intermediate result we establish a quantitative Alexandrov type estimate for normal deformations of a ball. Finally, we provide existence for flat flows as limit points of the discrete flow when the time discretization parameter tends to zero.

Subjects / Keywords

Geometric evolutions; Fractional mean curvature; Alexandrov theorem; Minimizing movements; Variational methods