Generalized maximum principles and the unicity of complete spacelike hypersurfaces immersed in a Lorentzian product space

Abstract

We establish unicity results concerning complete spacelike hypersurfaces immersed in a Lorentzian product space, under appropriated restrictions on the norm of the gradient of the height function. Our approach is based on two analytical tools: the well known Omori–Yau generalized maximum principle, and another suitable maximum principle at the infinity due to Yau. As application of our unicity results, we study the rigidity of entire vertical graphs in such ambient spaces.