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

scholarly journals On Complete Spacelike Hypersurfaces in a Semi-Riemannian Warped Product

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Hyperbolic Space ◽  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
Height Function ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Entire Vertical Graphs ◽  
Spacelike Hypersurfaces

By applying Omori-Yau maximal principal theory and supposing an appropriate restriction on the norm of gradient of height function, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces with nonpositive constant mean curvature immersed in a semi-Riemannian warped product. Furthermore, some applications of our main theorems for entire vertical graphs in Robertson-Walker spacetime and for hypersurfaces in hyperbolic space are given.

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.

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
Sign in / Sign up

Export Citation Format

Share Document