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

TL;DR

This paper investigates the uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes, extending previous results to both compact and noncompact cases using advanced maximum principles.

Contribution

It extends the uniqueness results for spacelike hypersurfaces with constant higher order mean curvature to noncompact cases using a generalized Omori-Yau maximum principle.

Findings

Established uniqueness for compact spacelike hypersurfaces

Extended results to noncompact hypersurfaces

Applied generalized Omori-Yau maximum principle

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].