Complete Vertical Graphs with Constant Mean Curvature in Semi-Riemannian Warped Products

被引：52
|
作者：
Caminha, A. [1 ]
de Lima, H. F. [2 ]
机构：
[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil
[2] Univ Fed Campina Grande, Dept Matemat & Estatist, BR-58109970 Campinas Grande, Paraiba, Brazil
来源：
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2009年 / 16卷 / 01期
关键词：
Semi-Riemannian manifolds; Lorentz geometry; Hyperbolic space; Steady State space; Vertical graphs; Bernstein-type theorems; SPACELIKE HYPERSURFACES; SITTER SPACE; UNIQUENESS;
D O I：
10.36045/bbms/1235574194
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study complete vertical graphs of constant mean curvature in the Hyperbolic and Steady State spaces. We first derive suitable formulas for the Laplacians of the height function and of a support-like function naturally attached to the graph; then, under appropriate restrictions on the values of the mean curvature and the growth of the height function, we obtain necessary conditions for the existence of such a graph. In the two-dimensional case we apply this analytical framework to state and prove Bernstein-type results in each of these ambient spaces.
引用
收藏
页码：91 / 105
页数：15
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