Hypersurfaces of Constant Curvature in Hyperbolic Space I

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hypersurfaces with Constant Scalar Curvature in a Hyperbolic Space Form

Let M be a complete hypersurface with constant normalized scalar curvature R in a hyperbolic space form H. We prove that if R̄ = R + 1 ≥ 0 and the norm square |h| of the second fundamental form of M satisfies nR̄ ≤ sup |h| ≤ n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], then either sup |h| = nR̄ and M is a totally umbilical hypersurface; or sup |h| = n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], and M i...

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...

hypersurfaces with constant mean curvature in a lorentzian space form

Curvature Flow of Complete Convex Hypersurfaces in Hyperbolic Space

We investigate the existence, convergence and uniqueness of modified general curvature flow (MGCF) of convex hypersurfaces in hyperbolic space with a prescribed asymptotic boundary.