On the rigidity of constant mean curvature complete vertical graphs in warped products

被引：28
|
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：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2011年 / 29卷 / 04期
关键词：
Warped products; Hyperbolic space; Euclidean space; Complete vertical graphs; Constant mean curvature; Bernstein-type theorems; RIEMANNIAN-MANIFOLDS; SPACELIKE HYPERSURFACES; UNIQUENESS;
D O I：
10.1016/j.difgeo.2011.04.039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate constant mean curvature complete vertical graphs in a warped product, which is supposed to satisfy an appropriated convergence condition. In this setting, under suitable restrictions on the values of the mean curvature and the norm of the gradient of the height function, we obtain rigidity theorems concerning to such graphs. Furthermore, applications to the hyperbolic and Euclidean spaces are given. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码：590 / 596
页数：7
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