Higher genus mean curvature 1 catenoids in hyperbolic and de Sitter 3-spaces

Abstract

We show existence of constant mean curvature 1 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.

11 pages, 5 figures

Cited by in corpus (1)

• New maximal surfaces in Minkowski 3-space with arbitrary genus and their cousins in de Sitter 3-space