Convex sets evolving by volume preserving fractional mean curvature flows

Abstract

We consider the volume preserving geometric evolution of the boundary of a set under fractional mean curvature. We show that smooth convex solutions maintain their fractional curvatures bounded for all times, and the long time asymptotics approach round spheres. The proofs are based on apriori estimates on the inner and outer radii of the solutions.

References in corpus (3)

• Convergence of nonlocal threshold dynamics approximations to front propagation
• Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space
• Nonlocal minimal graphs in the plane are generically sticky

Cited by in corpus (1)

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