Spacelike hypersurfaces with functionally bounded mean curvature in Lorentzian warped products and generalized Calabi-Bernstein type problems

Abstract

We study spacelike hypersurfaces with functionally bounded mean curvature in Lorentzian warped products M = I × f F , where F is a (non-compact) complete Riemannian mani- fold whose universal covering is parabolic. In particular, we provide several rigidity results under appropriate mathematical and physical assumptions. As an application, several Calabi- Bernstein type results are obtained which widely extend the previous ones in this setting.