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.

Ciraolo, G., Figalli, A., Maggi, F., & Novaga, M. (2018). Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2018(741), 275-294 [10.1515/crelle-2015-0088].

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

CIRAOLO, Giulio;
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.
Settore MAT/05 - Analisi Matematica
https://www.degruyter.com/view/j/crelle.2018.2018.issue-741/crelle-2015-0088/crelle-2015-0088.xml?rskey=UK226F&result=9&q=ciraolo
Ciraolo, G., Figalli, A., Maggi, F., & Novaga, M. (2018). Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 2018(741), 275-294 [10.1515/crelle-2015-0088].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/150513
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