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


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


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.