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In this paper we provide several uniqueness and non-existence results forcomplete parabolic constant mean curvature spacelike hypersurfaces inLorentzian warped products under appropriate geometric assumptions. As aconsequence of this parametric study, we obtain very general uniqueness andnon-existence results for a large family of uniformly elliptic EDP's, sosolving the Calabi-Bernstein problem in a wide family of spacetimes.

Constant mean curvature spacelike hypersurfaces in Lorentzian warped products and Calabi-Bernstein type problems