LINEAR WEINGARTEN HYPERSURFACES WITH BOUNDED MEAN CURVATURE IN THE HYPERBOLIC SPACE

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

Linear Weingarten hypersurfaces in a unit sphere

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

Uniqueness of Starshaped Compact Hypersurfaces With Prescribed m-th Mean Curvature in Hyperbolic Space

Let ψ be a given function defined on a Riemannian space. Under what conditions does there exist a compact starshaped hypersurfaceM for which ψ, when evaluated onM , coincides with them−th elementary symmetric function of principal curvatures of M for a given m? The corresponding existence and uniqueness problems in Euclidean space have been investigated by several authors in the mid 1980’s. Rec...

STARSHAPED COMPACT HYPERSURFACES WITH PRESCRIBED k-TH MEAN CURVATURE IN HYPERBOLIC SPACE

In this paper we consider the problem of finding a star-shaped compact hypersurface with prescribed k-th mean curvature in hyperbolic space. Under some sufficient conditions, we obtain an existence result by establishing a priori estimates and using degree theory arguments.