数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (1): 353-360.doi: 10.1016/S0252-9602(11)60235-X

• 论文 • 上一篇    

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

邓勤涛   

  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
  • 收稿日期:2009-04-23 修回日期:2009-10-20 出版日期:2011-01-20 发布日期:2011-01-20
  • 基金资助:

    Research was supported by NSFC (10901067) and partially supported by NSFC (10801058) and Hubei Key Laboratory of Mathematical Sciences

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

摘要:

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].

关键词: k-weighted bi-Ricci curvature, finite index, constant mean curvature

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

中图分类号: 

  • 53C40