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Attaching handles to Bryant surfaces

Frank Pacard·Fernando A. A. Pimentel
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Abstract

We prove the existence of complete, embedded, constant mean curvature 1 surfaces in 3 dimensional hyperbolic space when g, the genus of the surface, and n, the number of ends of the surface, satisfy either g=0 and $n\geq 1$ or $g \geq 1$ and $2n\geq g+5$. The surfaces are all regular points of their corresponding moduli space.

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Frank Pacard, Fernando A. A. Pimentel. 2001-12-20. Attaching handles to Bryant surfaces. https://arxiv.org/abs/math/0112224

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