Published Paper

Inserted: 13 jan 2022
Last Updated: 2 mar 2023

Journal: Calculus of Variations and Partial Differential Equations
Year: 2023
Doi: https://doi.org/10.1007/s00526-023-02439-0

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.