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 / G. Ciraolo, A. Figalli, F. Maggi, M. Novaga. - In: JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK. - ISSN 0075-4102. - 741(2018), pp. 275-294. [10.1515/crelle-2015-0088]
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
G. Ciraolo;
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 C2-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.File | Dimensione | Formato | |
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19 - Ciraolo_Figalli_Maggi_Novaga_Crelle.pdf
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Nonlocal_Alexandrov_revised.pdf
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