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arXiv · 1503.00653

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

Giulio Ciraolo·Alessio Figalli·Francesco Maggi·Matteo Novaga
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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.

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Giulio Ciraolo, Alessio Figalli, Francesco Maggi, Matteo Novaga. 2015-03-02. Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature. https://arxiv.org/abs/1503.00653

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