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arXiv · 0904.3988

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

Shoichi Fujimori·Wayne Rossman
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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.

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Shoichi Fujimori, Wayne Rossman. 2010-02-25. Higher genus mean curvature 1 catenoids in hyperbolic and de Sitter 3-spaces. https://arxiv.org/abs/0904.3988

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