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Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson–Walker spacetimes

Published online by Cambridge University Press:  20 October 2011

LUIS J. ALÍAS
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain. e-mail: ljalias@um.es
DEBORA IMPERA
Affiliation:
Dipartimento di Matematica, Università degli studi di Milano, Via Saldini 50, I-20133 Milano, Italy. e-mail: debora.impera@unimi.it and marco.rigoli@unimi.it
MARCO RIGOLI
Affiliation:
Dipartimento di Matematica, Università degli studi di Milano, Via Saldini 50, I-20133 Milano, Italy. e-mail: debora.impera@unimi.it and marco.rigoli@unimi.it

Abstract

In this paper we analyse the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson–Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing some previous results given in [2]. We next extend these results to the complete noncompact case. In that case, our approach is based on the use of a generalized version of the Omori–Yau maximum principle for trace type differential operators, recently given by the authors in [3].

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2011

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