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VOL. 34 | 2002 The Gaussian Image of Mean Curvature One Surfaces in $\mathbb{H}^3$ of Finite Total Curvature
Pascal Collin, Laurent Hauswirth, Harold Rosenberg

Editor(s) Kenji Fukaya, Seiki Nishikawa, Joel Spruck

Abstract

The hyperbolic Gauss map $G$ of a complete constant mean curvature one surface $M$ in hyperbolic 3-space, is a holomorphic map from $M$ to the Riemann sphere. When $M$ has finite total curvature, we prove $G$ can miss at most three points unless $G$ is constant. We also prove that if $M$ is a properly embedded mean curvature one surface of finite topology, then $G$ is surjective unless $M$ is a horosphere or catenoid cousin.

Information

Published: 1 January 2002
First available in Project Euclid: 31 December 2018

zbMATH: 1030.53018
MathSciNet: MR1925732

Digital Object Identifier: 10.2969/aspm/03410009

Subjects:
Primary: 53A10
Secondary: 53A35

Rights: Copyright © 2002 Mathematical Society of Japan

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