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ON THE EXISTENCE OF $f$-MAXIMAL SPACELIKE HYPERSURFACES IN CERTAIN WEIGHTED MANIFOLDS
Part of
ARLANDSON M. S. OLIVEIRA, HENRIQUE F. DE LIMA
Journal:

Bulletin of the Australian Mathematical Society / Volume 96 / Issue 2 / October 2017

Published online by Cambridge University Press:

02 May 2017, pp. 317-325

Print publication:

October 2017
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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.