Attaching handles to Bryant surfaces

2001/12/20 by Frank Pacard, Pacard, Frank, Fernando A. A. Pimentel +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/0112224

arxiv created 2001/12/20 · arxiv updated 2009/11/30

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≥ 1 or g ≥ 1 and 2n≥ g+5. The surfaces are all regular points of their corresponding moduli space.

Related

• Spacelike mean curvature 1 surfaces of genus 1 with two ends in de Sitter 3-space
• The geometry of finite topology Bryant surfaces
• Attaching handles to Delaunay nodo"ıds
• Monodromy of constant mean curvature surface in hyperbolic space
• Constant Mean Curvature surfaces with prescribed finite topologies