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

作　　者：邓勤涛 

机构地区：[1]Department of Mathematics, Sun Yat-Sen University [2]Laboratory of Nonlinear Analysis, and School of Mathematics and Statistics,Huazhong Normal University

出　　处：《Acta Mathematica Scientia》2011年第1期353-360,共8页数学物理学报（B辑英文版）

基　　金：supported by NSFC (10901067);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 6634 （H2 114785 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 6643 （resp. H2 114785 ） must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].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 6634 （H2 114785 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 6643 （resp. H2 114785 ） 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 

分 类 号：O186.11[理学—数学]