# Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature

created by figalli on 02 Mar 2015
modified by novaga on 01 Aug 2018

[BibTeX]

Published Paper

Inserted: 2 mar 2015
Last Updated: 1 aug 2018

Journal: J. Reine Angew. Math.
Volume: 741
Pages: 275-294
Year: 2018
Doi: https://doi.org/10.1515/crelle-2015-0088

ArXiv: 1503.00653 PDF

Abstract:

We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its $C^2$-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.