Constant mean curvature surface, harmonic maps, and universal Teichmüller space

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form

The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces

We examine the space of surfaces in R which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space Mk of all such surfaces with k ends (where surfaces are identified if they differ by an isometry of R) is locally a real analytic variety. When the linearization of the quasil...

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...

Embedded Constant Mean Curvature Surfaces in Euclidean Three-space

In this paper we refine the construction and related estimates for complete Constant Mean Curvature surfaces in Euclidean three-space developed in [12] by adopting the more precise and powerful version of the methodology which was developed in [16]. As a consequence we remove the severe restrictions in establishing embeddedness for complete Constant Mean Curvature surfaces in [12] and we produc...