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The value distribution of the hyperbolic Gauss map
Author(s):
Zu-Huan
Yu
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2997-3001.
MSC (1991):
Primary 53A10;
Secondary 53C42
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Abstract:
In this paper, we investigate the hyperbolic Gauss map of a complete CMC-1 surface in  , and prove that it cannot omit more than four points unless the surface is a horosphere.
References:
- 1.
- R. L. Bryant, Surfaces of mean curvature one in hyperbolic space, Asterisque 154-155 (1987), 321-347. CMP 20:16
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- R. Osserman, Minimal surfaces in the large, Comment. Math. Helv. 35 (1961), 65-76. MR 23:A576
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- M. Umehara and K. Yamada, Complete surfaces of constant mean curvature-
 in the hyperbolic  -space, Ann. of Math. 137 (1993), 611-638. MR 94c:53015 - 5.
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 into the hyperbolic  -space, J. Reine Angew. Math. 432 (1992), 93-116. MR 94e:54004 - 6.
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- 8.
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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
DOI:
10.1090/S0002-9939-97-03937-3
PII:
S 0002-9939(97)03937-3
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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