Meridian Surfaces with Constant Mean Curvature in Pseudo-Euclidean 4-Space with Neutral Metric

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

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...

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...

hypersurfaces with constant mean curvature in a lorentzian space form

Constant Mean Curvature Surfaces in Euclidean and Minkowski 3-spaces

Spacelike constant mean curvature surfaces in Minkowski 3-space L have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for constant mean curvature surfaces in Euclidean space, replacing the group SU(2) with SU(1, 1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop grou...