TOTALLY SYMMETRIC SURFACES OF CONSTANT MEAN CURVATURE IN HYPERBOLIC 3-SPACE

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...

Symmetric Surfaces of Constant Mean Curvature in 3

Surfaces of Revolution with Constant Mean Curvature in Hyperbolic 3-Space

In this paper, we construct surfaces of revolution with constant mean curvature H = c and minimal surfaces of revolution in hyperbolic 3-space H(−c) of constant sectional curvature −c. It is shown that surfaces of revolution with constant mean curvature H = c in H(−c) tend toward the catenoid, the minimal surface of revolution in Euclidean 3-space E as c → 0. Minimal surfaces of revolution in H...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

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...