A new approach for uniqueness of complete maximal hypersurfaces in spatially parabolic GRW spacetimes

Complete maximal hypersurfaces in Generalized Robertson–Walker spacetimes whose fiber has a parabolic universal Riemannian covering are studied. Under natural boundedness assumptions, a spacelike hypersurface is shown to be parabolic when it is endowed with a conformal metric. This fact allows us to get, for complete maximal hypersurfaces, several uniqueness results. As an application, all the entire solutions to the maximal hypersurface equation under certain constrains are obtained, solving new Calabi–Bernstein problems.