Ramification estimates for the hyperbolic Gauss map

Details Ramification estimates for the hyperbolic Gauss map Ramification estimates for the hyperbolic Gauss map

2008-04-03

arxiv.org/abs/0804.0470v4

Osaka J. Math., 46 (2009), 1059-1076

Mathematics

Differential Geometry

16 pages, corrected some typos. OCAMI Preprint Series 08-1, to appear in Osaka Journal of Mathematics

Scientific paper

We give the best possible upper bound on the number of exceptional values and the totally ramified value number of the hyperbolic Gauss map for pseudo-algebraic constant mean curvature one surfaces in the hyperbolic three-space and some partial results on the Osserman problem for algebraic case. Moreover, we study the value distribution of the hyperbolic Gauss map for complete constant mean curvature one faces in de Sitter three-space.

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