Calculus of Variations and Geometric Measure Theory

D. De Gennaro - A. Kubin - A. Kubin

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

created by degennaro on 18 Apr 2022
modified on 12 Jan 2023

[BibTeX]

Published Paper

Inserted: 18 apr 2022
Last Updated: 12 jan 2023

Journal: Nonlinear Anal.
Year: 2022
Doi: 10.1016/j.na.2022.113200

ArXiv: 2204.07450 PDF
Links: Arxiv link

Abstract:

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.