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|Title:||Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space|
|Citation:||Cheung, L.-F.,Leung, P.-F. (2001-03). Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space. Mathematische Zeitschrift 236 (3) : 525-530. ScholarBank@NUS Repository.|
|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 α < n-1. We prove in this paper that λ1 (M) ≥ 1/4 (n - 1 - α)2 > 0. In particular when M is minimal we have λ1 (M) ≥ 1/4 (n - 1)2 and this is sharp because equality holds when M is totally geodesic.|
|Source Title:||Mathematische Zeitschrift|
|Appears in Collections:||Staff Publications|
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