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 C2-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.

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

Novaga, Matteo
2018-01-01

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 C2-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.
2018
Ciraolo, Giulio; Figalli, Alessio; Maggi, Francesco; Novaga, Matteo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/926348
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