Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space |
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| Authors: | Leung-Fu Cheung Pui-Fai Leung |
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| Institution: | (1) Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hum, Kowloon, Hong Kong (e-mail: malfcheu@inet.polyu.edu.hk) , HK;(2) Department of Mathematics, National University of Singapore, Lower Kent Ridge Road, Singapore 119260 (e-mail: matfredl@nus.edu.sg) , SG |
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| Abstract: | Let M be an n-dimensional complete non-compact submanifold in a hyperbolic space with the norm of its mean curvature vector bounded by
a constant . We prove in this paper that . In particular when M is minimal we have and this is sharp because equality holds when M is totally geodesic.
Received September 14, 1999; in final form November 12, 1999 / Published online December 8, 2000 |
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| Keywords: | Mathematics Subject Classification (1991): 53C20 |
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