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The value distribution of the hyperbolic Gauss map

Author: Zu-Huan Yu
Journal: Proc. Amer. Math. Soc. 125 (1997), 2997-3001
MSC (1991): Primary 53A10; Secondary 53C42
MathSciNet review: 1401758
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Abstract: In this paper, we investigate the hyperbolic Gauss map of a complete CMC-1 surface in $H^3(-1)$, and prove that it cannot omit more than four points unless the surface is a horosphere.

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Additional Information

Zu-Huan Yu
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Address at time of publication: Fundamental Department, Jiaozuo Institute of Technology, Jiaozuo 454159, Henan Province, People’s Republic of China

Keywords: Constant mean curvature, hyperbolic space, Gauss map.
Received by editor(s): November 1, 1995
Received by editor(s) in revised form: April 2, 1996
Additional Notes: Partially supported by NNSFC and SFECC
Communicated by: Christopher Croke
Article copyright: © Copyright 1997 American Mathematical Society