lorentzian product space
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ON THE EXISTENCE OF -MAXIMAL SPACELIKE HYPERSURFACES IN CERTAIN WEIGHTED MANIFOLDS

2017 ◽  
Vol 96 (2) ◽  
pp. 317-325
Author(s):  
ARLANDSON M. S. OLIVEIRA ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Product Space ◽  
Mean Value ◽  
Sobolev Embedding ◽  
Lorentzian Manifolds ◽  
Heat Operator ◽  
Nonexistence Result ◽  
Spacelike Hypersurfaces ◽  
Mean Value Inequality ◽  
Weighted Manifolds ◽  
Lorentzian Product Space

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.

Complete CMC spacelike hypersurfaces immersed in a Lorentzian product space

2015 ◽  
Vol 104 (6) ◽  
pp. 577-587 ◽  
Author(s):  
Cícero P. Aquino ◽  
Henrique F. de Lima ◽  
Eraldo A. Lima
Keyword(s):  
Product Space ◽  
Spacelike Hypersurfaces ◽  
Lorentzian Product Space
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