Abstract
Complete spacelike hypersurfaces in spatially parabolic standard static spacetimes are studied. Under natural boundedness assumptions, we show how the parabolicity of the base is inherited by any spacelike hypersurface and vice versa. Moreover, we give new uniqueness and non-existence results for complete spacelike hypersurfaces in these ambient spacetimes as well as solve new Calabi–Bernstein-type problems.
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