Rearrangements and radial graphs of constant mean curvature in hyperbolic space

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.

Graphs of Constant Mean Curvature in Hyperbolic Space

We study the problem of finding constant mean curvature graphs over a domain of a totally geodesic hyperplane and an equidistant hypersurface Q of hyperbolic space. We find the existence of graphs of constant mean curvature H over mean convex domains ⊂ Q and with boundary ∂ for −H∂ < H ≤ |h|, where H∂ > 0 is the mean curvature of the boundary ∂ . Here h is the mean curvature respectively of the...

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...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Constant Mean Curvature Surfaces with Two Ends in Hyperbolic Space

We investigate the close relationship between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. Just as in the case of minimal surfaces in Euclidean 3-space, the only complete connected embedded constant mean curvature 1 surfaces with two ends in hyperbolic space are well-understood surfaces of revolution – the catenoid cousins. In contrast to t...