On the evolution by fractional mean curvature

2015/11/22 by Sáez, Mariel, Valdinoci, Enrico · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.06944

Abstract

In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions equations for fractional geometric quantities that yield preservation of certain quantities (such as positive fractional curvature) and smoothness of graphical evolutions.

Cited by

• The strongly nonlocal Allen-Cahn problem

Related

• Short time existence of the classical solution to the fractional Mean curvature flow
• Stability results for nonlocal geometric evolutions and limit cases for\n fractional mean curvature flows
• Neckpinch singularities in fractional mean curvature flows
• Convergence of the volume preserving fractional mean curvature flow for convex sets
• Time-fractional Allen-Cahn equations versus powers of the mean curvature