Acta mathematica scientia, Series B >
COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES
Received date: 2009-04-23
Revised date: 2009-10-20
Online published: 2011-01-20
Supported by
Research was supported by NSFC (10901067) and partially supported by NSFC (10801058) and Hubei Key Laboratory of Mathematical Sciences
In this article, we prove that any complete finite index hypersurface in the hyperbolic space H4(−1)(H5(−1)) with constant mean curvature H satisfying H2 > 64/63(H2 > 175/148 respectively) must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H4(−1) (resp. H5(−1)) with constant mean curvature H satisfying H2 > 64/63 (resp. H2 > 175/148 ) must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].
DENG Qin-Tao . COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 353 -360 . DOI: 10.1016/S0252-9602(11)60235-X
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