HIGHER-GENUS MEAN CURVATURE-ONE CATENOIDS IN HYPERBOLIC AND DE SITTER 3-SPACES

摘要

We show the existence of constant mean curvature-one surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior.