Abstract
We apply a mean-value inequality for positive subsolutions of the $f$-heat operator, obtained from a Sobolev embedding, to prove a nonexistence result concerning complete noncompact $f$-maximal spacelike hypersurfaces in a class of weighted Lorentzian manifolds. Furthermore, we establish a new Calabi–Bernstein result for complete noncompact maximal spacelike hypersurfaces in a Lorentzian product space.
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