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A Bernstein-type theorem in hyperbolic spaces

Published online by Cambridge University Press:  26 February 2010

Sung-Eun Koh
Affiliation:
Department of Mathematics, Konkuk University, Seoul, 143–701, Korea. e-mail: sekoh@kkucc.konkuk.ac.kr
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Abstract

The following Bernstein-type theorem in hyperbolic spaces is proved. Let ∑ be a non-zero constant mean curvature complete hypersurface in the hyperbolic space ℍn. Suppose that there exists a one-to-one orthogonal projection from ∑ into a horosphere. (1) If the projection is surjective, then ∑ is a horosphere. (2) If the projection is not surjective and its image is simply connected, then ∑ is a hypersphere.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1999

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References

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