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

Rigidity and Sharp Stability Estimates for Hypersurfaces with Constant and Almost-constant Nonlocal Mean Curvature

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-distance from a single sphere. The corresponding stability inequality is obtained with a shar...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Stability of Hypersurfaces with Constant R-th Anisotropic Mean Curvature

Given a positive function F on S which satisfies a convexity condition, we define the r-th anisotropic mean curvature function H r for hypersurfaces in R n+1 which is a generalization of the usual r-th mean curvature function. Let X : M → R be an n-dimensional closed hypersurface with H r+1 =constant, for some r with 0 ≤ r ≤ n− 1, which is a critical point for a variational problem. We show tha...

Constant Mean Curvature Hypersurfaces with Constant Δ-invariant

We completely classify constant mean curvature hypersurfaces (CMC) with constant δ-invariant in the unit 4-sphere S 4 and in the Euclidean 4-space E 4 .

hypersurfaces with constant mean curvature in a lorentzian space form