Constant mean curvature spacelike hypersurfaces in Lorentzian warped   products and Calabi-Bernstein type problems
  In this paper we provide several uniqueness and non-existence results for complete parabolic constant mean curvature spacelike hypersurfaces in Lorentzian warped products under appropriate geometric assumptions. As a consequence of this parametric study, we obtain very general uniqueness and non-existence results for a large family of uniformly elliptic EDP's, so solving the Calabi-Bernstein problem in a wide family of spacetimes. 
Juan A. Aledo, Alfonso Romero and Rafael M. Rubio
math.DG gr-qc