Graphs of Constant Mean Curvature in Hyperbolic Space

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hyperbolic surfaces of $L_1$-2-type

In this paper, we show that an $L_1$-2-type surface in the three-dimensional hyperbolic space $H^3subset R^4_1$ either is an open piece of a standard Riemannian product $ H^1(-sqrt{1+r^2})times S^{1}(r)$, or it has non constant mean curvature, non constant Gaussian curvature, and non constant principal curvatures.

Rearrangements and Radial Graphs of Constant Mean Curvature in Hyperbolic Space

We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results are proved via rearrangement techniques.

Existence of constant mean curvature graphs in hyperbolic space

We give an existence result for constant mean curvature graphs in hyperbolic space Hn+1. Let Ω be a compact domain of a horosphere in Hn+1 whose boundary ∂Ω is mean convex, that is, its mean curvature H∂Ω (as a submanifold of the horosphere) is positive with respect to the inner orientation. If H is a number such that −H∂Ω < H < 1, then there exists a graph over Ω with constant mean curvature H...

On the Geometry of Constant Mean Curvature One Surfaces in Hyperbolic Space

We give a geometric classification of regular ends with constant mean curvature 1 and finite total curvature, embedded in hyperbolic space. We prove that each such end is either asymptotic to a catenoid cousin or asymptotic to a horosphere. We also study symmetry properties of constant mean curvature 1 surfaces in hyperbolic space associated to minimal surfaces in Euclidean space. We describe t...