ON STABLE CONSTANT MEAN CURVATURE HYPERSURFACES

被引：3

作者：

Fu, Hai-Ping ^{[1
]}

Li, Zhen-Qi ^{[1
]}

机构：

[1] Nanchang Univ, Dept Math, Nanchang 330047, Peoples R China

来源：

TOHOKU MATHEMATICAL JOURNAL | 2010年 / 62卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Stable hypersurface; L(2) harmonic forms; constant mean curvature; harmonic map; ends; L-2; HARMONIC; 1-FORMS; MINIMAL HYPERSURFACES; COMPLETE SUBMANIFOLDS; RIEMANNIAN-MANIFOLDS; EUCLIDEAN-SPACE; FINITE INDEX; STABILITY; SURFACES; RN+1;

D O I：

10.2748/tmj/1287148618

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study complete non-compact stable constant mean curvature hypersurfaces in a Riemannian manifold of bounded geometry, and prove that there are no nontrivial L(2) harmonic 1-forms on such hypersurfaces. We also show that any smooth map with finite energy from such a hypersurface to a compact manifold with non-positive sectional curvature is homotopic to constant on each compact set. In particular, we obtain some one-end theorems of complete non-compact weakly stable constant mean curvature hypersurfaces in the space forms.

引用

页码：383 / 392

页数：10