The geometry of finite topology Bryant surfaces
Differential Geometry
2007-05-23 v1
Abstract
In this paper we shall establish that properly embedded constant mean curvature one surfaces in H^3 of finite topology are of finite total curvature and each end is regular. In particular, this implies the horosphere is the only simply connected such example, and the catenoid cousins the only annular examples of this nature. In general each annular end of such a surface is asymptotic to an end of a horosphere or an end of a catenoid cousin.
Keywords
Cite
@article{arxiv.math/0105265,
title = {The geometry of finite topology Bryant surfaces},
author = {Pascal Collin and Laurent Hauswirth and Harold Rosenberg},
journal= {arXiv preprint arXiv:math/0105265},
year = {2007}
}
Comments
37 pages, published version