The geometry of finite topology Bryant surfaces

By P. Collin, L. Hauswirth, H. Rosenberg. 2001

74 citations recorded by the source corpus.

We prove that in the three dimensional hyperbolic space H(3) the properly embedded constant mean curvature one surfaces with finite topology are of finite total curvature and each ends are regular. This imply in particular that the hrosphere is the only properly embedded simply connected constant mean curvature one surface in H(3).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/02ff967208098aaa5fc7e0b22e7ac6741d9dd20a

How researchers see this paper

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In Applied Mathematics

1. I. Fernández
2. Pablo Mira
3. U. Abresch
4. H. Rosenberg
5. Benoît Daniel
6. L. Hauswirth
7. Ricardo Sa Earp
8. W. H. Meeks

In Geometry and Topology

1. I. Fernández
2. Pablo Mira
3. H. Rosenberg
4. U. Abresch
5. Benoît Daniel
6. Ricardo Sa Earp
7. L. Hauswirth
8. W. H. Meeks

Citations in the corpus

• A Hopf differential for constant mean curvature surfaces inS2×R andH2×R (2004, background): “For cmc surfaces E2g of genus g > l the holomorphic quadratic differential still provides a link between the genus of the surface and the number and index of its umbilics, a link tha t has been very useful in investigating the geometric properties of such cme surfaces (see [8], [11] and [22]).”
• Harmonic maps and constant mean curvature surfaces in H 2 x R (2007, background): “their geometry has been studied in great detail (see for instance [Bry, UmYa2, UmYa1, UmYa3, CHR , HRR, GaMi] and references therein).”