On Bernstein-type properties of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime
type: Item
instance of: scholarly article
title: On Bernstein-type properties of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime
zbMATH Open document ID: 1271.53055
author: Henrique Fernandes de Lima
published in: Journal of Geometry
publication date: 2012-12-27T00:00:00Z
review text: Applying the well-known Omori-Yau generalized maximum principle ([\textit{H. Omori}, J. Math. Soc. Japan 19, 205--214 (1967; Zbl 0154.21501); \textit{S.-T. Yau}, Commun. Pure Appl. Math. 28, 201--228 (1975; Zbl 0291.31002)], a suitable extension was established in [\textit{A. Caminha} and the author, Gen. Relativ. Gravitation 41, No. 1, 173--189 (2009; Zbl 1162.83304)]), the author investigates Bernstein-type properties of complete space-like hypersurfaces immersed in a generalized Robertson-Walker space-time, which is supposed to obey a standard convergence condition.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 6118613
zbMATH Keywords: Bernstein-type properties
zbMATH Keywords: complete space-like hypersurfaces
zbMATH Keywords: Robertson-Walker space-time
reviewed by: Huafei Sun
MaRDI profile type: Publication
full work available at URL: s00022-012-0122-6
OpenAlex ID: W2050124775
cites work: Complete spacelike hypersurfaces in a Robertson–Walker spacetime
cites work: INTEGRAL FORMULAE FOR SPACELIKE HYPERSURFACES IN CONFORMALLY STATIONARY SPACETIMES AND APPLICATIONS
cites work: Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes
cites work: Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes
cites work: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
cites work: Constant mean curvature spacelike surfaces in three-dimensional generalized Robertson-Walker spacetimes
cites work: COMPLETE CMC SPACELIKE SURFACES WITH BOUNDED HYPERBOLIC ANGLE IN GENERALIZED ROBERTSON–WALKER SPACETIMES
cites work: Uniqueness of maximal surfaces in generalized Robertson-Walker spacetimes and Calabi-Bernstein type problems
cites work: Q5612020
cites work: Complete spacelike hypersurfaces in conformally stationary Lorentz manifolds
cites work: Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
cites work: Isometric immersions of Riemannian manifolds
cites work: On the mean curvature of spacelike surfaces in certain three-dimensional Robertson-Walker spacetimes and Calabi-Bernstein's type problems
DOI: 10.1007/S00022-012-0122-6
description: scientific article; zbMATH DE number 6118613