On the Gauss map of complete CMC hypersurfaces in the hyperbolic space

被引：14

作者：

Aquino, C. F. ^{[2
]}

de Lima, H. F. ^{[1
]}

机构：

[1] Univ Fed Campina Grande, Dept Matemat & Estat, BR-58109970 Campina Grande, Paraiba, Brazil

[2] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 386卷 / 02期

关键词：

Hyperbolic space; Complete hypersurfaces; Mean curvature; Gauss map; Hyperbolic cylinders; CONSTANT MEAN-CURVATURE; COMPLETE RIEMANNIAN MANIFOLDS; SITTER SPACE; INEQUALITY; GRAPHS;

D O I：

10.1016/j.jmaa.2011.08.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, as suitable applications of the so-called Omori-Yau generalized maximum principle, we obtain rigidity results concerning to complete hypersurfaces with constant mean curvature in the hyperbolic space, under appropriated restrictions on their Gauss image. Furthermore, by supposing a linear dependence between support functions naturally attached to such hypersurfaces, we establish a characterization theorem. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：862 / 869

页数：8

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