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

被引：0

作者：

Deng Qintao ^{[1
,2
,3
]}

机构：

[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Huazhong Normal Univ, Lab Nonlinear Anal, Wuhan 430079, Peoples R China

[3] Huazhong Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2011年 / 31卷 / 01期

关键词：

k-weighted bi-Ricci curvature; finite index; constant mean curvature; RIEMANNIAN-MANIFOLDS; MINIMAL-SURFACES; STABILITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we prove that any complete finite index hypersurface in the hyperbolic space H(4)(-1)(H(5)(-1)) with constant mean curvature H satisfying H(2) > 64/63 (H(2) > 175/148 respectively) must be compact. Specially, we verify that any complete and stable hypersurface in the hyperbolic space H(4)(-1) (resp. H(5)(-1)) with constant mean curvature H satisfying H(2) > 64/63 (resp. H(2) > 175/148) must be compact. It shows that there is no manifold satisfying the conditions of some theorems in [7, 9].

引用

页码：353 / 360

页数：8

共 18 条

[1]

Alencar H., 1994, An. Acad. Brasil. Cienc, V66, P265

[2]

[Anonymous], INVENT MATH

[3] STABILITY OF HYPERSURFACES OF CONSTANT MEAN-CURVATURE IN RIEMANNIAN-MANIFOLDS [J].