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A Bernstein‐type theorem in hyperbolic spaces
Author(s) -
Koh Sung-Eun
Publication year - 1999
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007579
Subject(s) - mathematics , surjective function , projection (relational algebra) , hypersurface , hyperbolic space , hyperbolic manifold , type (biology) , mathematical analysis , pure mathematics , zero (linguistics) , hyperbolic function , ecology , linguistics , philosophy , algorithm , biology
The following Bernstein‐type theorem in hyperbolic spaces is proved. Let ∑ be a non‐zero constant mean curvature complete hypersurface in the hyperbolic space ℍ n . 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.
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