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Geometry and Applications
March 13-16, 2000
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University
Novosibirsk, Russia

Organizers
Yu.G. Rushetnyak (Chair of Program Committee; Russia), V.V. Vershinin (Chair of Organizing Committee; Russia), A.A. Borisenko (Ukraine), Yu.D. Burago (Russia), V.M. Gol'dshtein (Israel), M.L. Gromov (France), I.G. Nikolaev (USA/Russia), S.P. Novikov (USA/Russia), A.V. Pogorelov (Ukraine), I.Kh. Sabitov (Russia)

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The geometry of finite topology surfaces properly embedded in hyperbolic space with constant mean curvature one
by
Harold Rosenberg
University of Paris 7, Paris, France
Coauthors: Pascal Collin, Laurent Hauswirth

A Bryant surface is a mean curvature one surface in hyperolic 3-space. In this talk I will discuss the structure of properly embedded Bryant surfaces of finite topology. We have proved ( in collaboration with Pascal Collin and Laurent Hauswirth) that these surfaces have finite total curvature, and each end is asymptotic to a horosphere or catenoid cousin end. In particular the only such simply connected Bryant surface is a horosphere.

Date received: February 22, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadw-40.