Quantitative stability for hypersurfaces with almost constant curvature in space forms

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hypersurfaces of Constant Curvature in Space Forms

In this paper we shall discuss hypersurfaces M of space forms of constant curvature; where curvature means one of the symmetric functions of curvature associated to the second fundamental form. The values of the constant will be chosen so that the linearized equation will be an elliptic equation onM . For example, for surfaces in 3 the two possible curvatures are the mean curvature H and the Ga...

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

Real Hypersurfaces with Constant Totally Real Bisectional Curvature in Complex Space Forms

In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space formMm(c), c 6= 0 as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11].