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

Giulio Ciraolo; Alessio Figalli; Matteo Novaga; Francesco Maggi

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

Giulio Ciraolo, Alessio Figalli, Matteo Novaga, Francesco Maggi

Matematica e Informatica

Risultato della ricerca: Article › peer review

22 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 originale	English
pagine (da-a)	275-294
Numero di pagine	20
Rivista	JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume	2018
Stato di pubblicazione	Published - 2018

All Science Journal Classification (ASJC) codes

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Applied Mathematics

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

author = "Giulio Ciraolo and Alessio Figalli and Matteo Novaga and Francesco Maggi",

year = "2018",

language = "English",

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T1 - Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature

AU - Ciraolo, Giulio

AU - Figalli, Alessio

AU - Novaga, Matteo

AU - Maggi, Francesco

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/150513

UR - https://www.degruyter.com/view/j/crelle.2018.2018.issue-741/crelle-2015-0088/crelle-2015-0088.xml?rskey=UK226F&result=9&q=ciraolo

M3 - Article

VL - 2018

SP - 275

EP - 294

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

ER -