Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (1): 353-360.doi: 10.1016/S0252-9602(11)60235-X

• Articles • Previous Articles    

COMPLETE HYPERSURFACES WITH CONSTANT MEAN CURVATURE AND FINITE INDEX IN HYPERBOLIC SPACES

 DENG Qin-Tao   

  1. Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China; Lboratory of Nonlinear Analysis, and School of Mathematics and Statistics,Huazhong Normal University, Wuhan 430079, China
  • Received:2009-04-23 Revised:2009-10-20 Online:2011-01-20 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

Abstract:

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].

Key words: k-weighted bi-Ricci curvature, finite index, constant mean curvature

CLC Number: 

  • 53C40
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