Accepted Paper

Inserted: 23 nov 2018
Last Updated: 12 sep 2019

Journal: Analysis & PDE
Year: 2018

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.

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