Search results for " Nonlocal mean curvature"

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

2018

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.

Mathematics - Differential GeometryMean curvatureApplied MathematicsGeneral Mathematics010102 general mathematicsMathematical analysis01 natural sciencesStability (probability)010101 applied mathematicsMathematics - Analysis of PDEsRigidity (electromagnetism)Differential Geometry (math.DG)Alexandrov Theorem Stability Nonlocal mean curvature fractional perimeterSettore MAT/05 - Analisi MatematicaFOS: MathematicsMathematics (all)0101 mathematicsConstant (mathematics)Mathematics (all); Applied MathematicsAnalysis of PDEs (math.AP)MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
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