6533b824fe1ef96bd128024a
RESEARCH PRODUCT
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
Alessio FigalliMatteo NovagaGiulio CiraoloFrancesco Maggisubject
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)Mathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 | Journal für die reine und angewandte Mathematik (Crelles Journal) |