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

Giulio Ciraolo, Alessio Figalli, Matteo Novaga, Francesco Maggi

Risultato della ricerca: Article

17 Citazioni (Scopus)

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.
Lingua originaleEnglish
pagine (da-a)275-294
Numero di pagine20
RivistaJOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume2018
Stato di pubblicazionePublished - 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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