Attaching handles to Bryant surfaces

Details Attaching handles to Bryant surfaces Attaching handles to Bryant surfaces

2001-12-20

arxiv.org/abs/math/0112224v1

Mathematics

Differential Geometry

Scientific paper

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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