Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Novaga

Fractional mean curvature flow of Lipschitz graphs

created by novaga on 21 Mar 2021
modified on 21 Feb 2023

[BibTeX]

Published Paper

Inserted: 21 mar 2021
Last Updated: 21 feb 2023

Journal: Manuscripta Mathematica
Volume: 170
Number: 3-4
Pages: 427-451
Year: 2023

ArXiv: 2103.11346 PDF

Abstract:

We consider the fractional mean curvature flow of entire Lipschitz graphs. We provide regularity results, and we study the long time asymptotics of the flow. In particular we show that in a suitable rescaled framework, if the initial graph is a sublinear perturbation of a cone, the evolution asymptotically approaches an expanding self-similar solution. We also prove stability of hyperplanes and of convex cones in the unrescaled case.