Stability of the ball under volume preserving fractional mean curvature flow

2022/04/11 by Annalisa Cesaroni, Cesaroni, Annalisa, Matteo Novaga +1
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.04923

openalex publication_date 2022/04/11 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28

Abstract

We consider the volume constrained fractional mean curvature flow of a nearly spherical set, and prove long time existence and asymptotic convergence to a ball. The result applies in particular to convex initial data, under the assumption of global existence. Similarly, we show exponential convergence to a constant for the fractional mean curvature flow of a periodic graph.

Related

• Convergence of the volume preserving fractional mean curvature flow for convex sets
• Short time existence of the classical solution to the fractional Mean\n curvature flow
• Fractional mean curvature flow of Lipschitz graphs
• Stability results for nonlocal geometric evolutions and limit cases for\n fractional mean curvature flows
• Long time behaviour of discrete volume preserving mean curvature flows