Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
type: Item
instance of: scholarly article
title: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
zbMATH Open document ID: 0908.53034
DOI: 10.1007/BF02105675
author: Alfonso Romero
author: Miguel Sánchez
author: Luis J. Alías
published in: General Relativity and Gravitation
publication date: 1995-02-26T00:00:00Z
review text: In Section 3, the relation between spacelike hypersurfaces and spacelike graphs in generalized Robertson-Walker spacetimes is given, and the conditions under which all these hypersurfaces are compact are studied. Section 4 contains two new integral formulas for compact spacelike hypersurfaces. In Section 5, a new technique to solve the problem: ``when is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice?'' is introduced. Finally, the natural conditions \(f'' \leq 0\) and \(\text{Ric} > (n - 1) (ff'' - f'{}^2)\) are imposed to solve a Bernstein-type problem.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 727347
zbMATH Keywords: spacelike graphs
zbMATH Keywords: generalized Robertson-Walker spacetimes
zbMATH Keywords: integral formulas
zbMATH Keywords: spacelike hypersurfaces
zbMATH Keywords: constant mean curvature
reviewed by: Petre Stavre
MaRDI profile type: Publication
cites work: Existence of maximal surfaces in asymptotically flat spacetimes
cites work: Isolated maximal surfaces in spacetime
cites work: Q4003026
cites work: Maximal space-like hypersurfaces in the Lorentz-Minkowski spaces
cites work: The Large Scale Structure of Space-Time
full work available at URL: https://doi.org/10.1007/bf02105675
OpenAlex ID: W3216478359
Recommended article: Q3150743
Recommended article: Uniqueness of noncompact spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes
Recommended article: Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes
Recommended article: Q3467090
Recommended article: Uniqueness of complete maximal hypersurfaces in spatially parabolic generalized Robertson-Walker spacetimes
Recommended article: Uniqueness of complete spacelike hypersurfaces via their higher order mean curvatures in a conformally stationary spacetime
Recommended article: Q4884337
Recommended article: Uniqueness of spacelike hypersurfaces of constant mean curvature in foliated spacetimes
Recommended article: Uniqueness of spacelike hypersurfaces in a GRW spacetime via higher order mean curvatures
Recommended article: Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes
description: scientific article; zbMATH DE number 727347