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A Bernstein-type theorem in hyperbolic spaces
Part of:
Global differential geometry
Published online by Cambridge University Press: 26 February 2010
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
Secondary:
53C40: Global submanifolds
- Type
- Research Article
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- Copyright
- Copyright © University College London 1999
References
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