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Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature.
- Source :
- Journal für die Reine und Angewandte Mathematik; 2018, Vol. 2018 Issue 741, p275-294, 20p
- Publication Year :
- 2018
-
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 {C^{2}} -distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00754102
- Volume :
- 2018
- Issue :
- 741
- Database :
- Complementary Index
- Journal :
- Journal für die Reine und Angewandte Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 131059867
- Full Text :
- https://doi.org/10.1515/crelle-2015-0088