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

Mathematics – Differential Geometry

Scientific paper

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11 pages, 5 figures

Scientific paper

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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