Uniqueness of maximal surfaces in Generalized Robertson-Walker spacetimes and Calabi-Bernstein type problems

被引：29

作者：

Caballero, Magdalena ^{[1
]}

Romero, Alfonso ^{[2
]}

Rubio, Rafael M. ^{[1
]}

机构：

[1] Univ Cordoba, Dept Math, E-14071 Cordoba, Spain

[2] Univ Granada, Dept Geometria & Topol, E-18071 Granada, Spain

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2010年 / 60卷 / 03期

关键词：

Spacelike surface; Zero mean curvature; Calabi-Bernstein problem; Generalized Robertson-Walker spacetimes; CONSTANT MEAN-CURVATURE; LORENTZ-MINKOWSKI SPACE; RIEMANNIAN MANIFOLDS; HYPERSURFACES; THEOREM;

D O I：

10.1016/j.geomphys.2009.11.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Complete maximal surfaces in Generalized Robertson-Walker spacetimes obeying either the Null Convergence Condition or the Timelike Convergence Condition are studied. Uniqueness theorems that widely extend the classical Calabi-Bernstein theorem, as well as previous results On complete maximal surfaces in Robertson-Walker spacetimes, i.e. the case in which the Gauss curvature of the fiber is a constant. are given. All the entire solutions to the maximal surface differential equation in certain Generalized Robertson-Walker spacetimes are found. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：394 / 402

页数：9

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