# Attaching handles to Bryant surfaces

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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https://hal.archives-ouvertes.fr/hal-00127007
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Submitted on : Saturday, January 27, 2007 - 3:53:28 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

### Citation

Frank Pacard, Fernando A. A. Pimentel. Attaching handles to Bryant surfaces. Journal de l'Institut de Mathématiques de Jussieu, 2004, 3, pp.421-459. ⟨hal-00127007⟩

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