Constant mean curvature spacelike hypersurfaces in Lorentzian manifolds with a timelike gradient conformal vector field

2011 ◽  
Vol 28 (14) ◽  
pp. 145009 ◽  
Author(s):  
Magdalena Caballero ◽  
Alfonso Romero ◽  
Rafael M Rubio
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Conformal Vector Field ◽  
Lorentzian Manifolds ◽  
Conformal Vector ◽  
Spacelike Hypersurfaces

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

2011 ◽  
Vol 151 (2) ◽  
pp. 271-282 ◽  
Author(s):  
ALMA L. ALBUJER ◽  
FERNANDA E. C. CAMARGO ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Rigidity Results ◽  
Complete Spacelike Hypersurfaces ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

scholarly journals Spacelike hypersurfaces of constant mean curvature and Calabi-Bernstein type problems

1997 ◽  
Vol 49 (3) ◽  
pp. 337-345 ◽  
Author(s):  
Luis J. Alías ◽  
Alfonso Romero ◽  
Miguel Sánchez
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Bernstein Type ◽  
Spacelike Hypersurfaces

Some remarks on the existence of spacelike hypersurfaces of constant mean curvature

1977 ◽  
Vol 82 (3) ◽  
pp. 489-495 ◽  
Author(s):  
A. J. Goddard
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
General Class ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurface ◽  
De Sitter Space ◽  
De Sitter ◽  
Minimal Graphs ◽  
Complete Spacelike Hypersurface ◽  
Spacelike Hypersurfaces

AbstractBernstein's theorem states that the only complete minimal graphs in R3 are the hyperplanes. We shall produce evidence in favour of some conjectural generalizations of this theorem for the cases of spacelike hypersurfaces of constant mean curvature in Minkowski space and in de Sitter space. The results suggest that the class of asymptotically simple space-times admitting a complete spacelike hypersurface of constant mean curvature may well be considerably smaller than the general class of asymptotically simple space-times.

Constant mean curvature spacelike hypersurfaces in standard static spaces: rigidity and parabolicity

2020 ◽  
Vol 49 (2) ◽  
pp. 297-323
Author(s):  
Eudes L. de LIMA ◽  
Henrique F. de LIMA ◽  
Eraldo A. LIMA Jr. ◽  
Adriano A. MEDEIROS
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Spacelike Hypersurfaces
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