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

Abstract

In this paper we analyze 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 in [3].

arXiv commentTo appear in Mathematical Proceedings of the Cambridge Philosophical Society

References in corpus (2)

• Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes
• Hypersurfaces of constant higher order mean curvature in warped products

Cited by in corpus (8)

• Generalized Robertson-Walker space times, a survey
• Comparison Theorems in Lorentzian Geometry and applications to spacelike hypersurfaces
• Hypersurfaces with constant curvature quotients in warped product manifolds
• Rigidity of spacelike hypersurfaces in spatially weighted generalized Robertson-Walker spacetimes
• Hypersurfaces of constant higher order mean curvature in warped products
• A general form of the weak maximum principle and some applications
• Spacetime closedness theorem for homogeneous Lorentzian foliations
• Higher order mean curvature estimates for bounded complete hypersurfaces