$\phi$-parabolicity and the uniqueness of spacelike hypersurfaces   immersed in a spatially weighted GRW spacetime
  In this paper, we extend a technique due to Romero, Rubio and Salamanca establishing sufficient conditions to guarantee the parabolicity of complete spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker spacetime whose fiber has phi-parabolic universal Riemannian covering. As some applications of this criteria, we obtain uniqueness results concerning spacelikes hypersurfaces immersed in spatially weighted generalized Robertson-Walker spacetimes. Furthermore, Calabi-Bernstein type results are also given. 
Alma L. Albujer, Henrique F. de Lima, Arlandson M. Oliveira and Marco   Antonio L. Vel\'asquez
math.DG