Calculus of Variations and Geometric Measure Theory

E. Cinti - C. Sinestrari - E. Valdinoci

Convex sets evolving by volume preserving fractional mean curvature flows

created by cinti on 23 Nov 2018
modified on 12 Sep 2019


Accepted Paper

Inserted: 23 nov 2018
Last Updated: 12 sep 2019

Journal: Analysis & PDE
Year: 2018


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.