A Bernstein-type theorem in hyperbolic spaces

Authors
Koh, SE
Citation
Se. Koh, A Bernstein-type theorem in hyperbolic spaces, MATHEMATIKA, 46(91), 1999, pp. 77-81
Citations number
5
Categorie Soggetti
Mathematics
Journal title
MATHEMATIKA
ISSN journal
00255793 → ACNP
Volume
46
Issue
91
Year of publication
1999
Part
1
Pages
77 - 81
Database
ISI
SICI code
0025-5793(199906)46:91<77:ABTIHS>2.0.ZU;2-Y
Abstract
The following Bernstein-type theorem in hyperbolic spaces is proved. Let Si gma be a non-zero constant mean curvature complete hypersurface in the hype rbolic space H-n. Suppose that there exists a one-to-one orthogonal project ion from Sigma into a horosphere. (1) If the projection is surjective, then Sigma is a horosphere. (2) If the projection is not surjective and its ima ge is simply connected, then Sigma is a hypersphere.