Monodromy of Constant Mean Curvature Surface in Hyperbolic Space

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...

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...

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...

Unitarization of Monodromy Representations and Constant Mean Curvature Trinoids in 3-dimensional Space Forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms R, S and H. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.