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

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. 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.