scholarly journals Constant mean curvature spacelike hypersurfaces in Lorentzian warped products and Calabi–Bernstein type problems

2014 ◽  
Vol 106 ◽  
pp. 57-69 ◽  
Author(s):  
Juan A. Aledo ◽  
Alfonso Romero ◽  
Rafael M. Rubio
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Warped Products ◽  
Bernstein Type ◽  
Spacelike Hypersurfaces

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 Complete spacelike hypersurfaces with positive r-th mean curvature in a semi-Riemannian warped product

2015 ◽  
Vol 23 (2) ◽  
pp. 259-277
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Ricci Curvature ◽  
Curvature Tensor ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
Comparison Inequality

Abstract In this paper, by supposing a natural comparison inequality on the positive r-th mean curvatures of the hypersurface, we obtain some new Bernstein-type theorems for complete spacelike hypersurfaces immersed in a semi-Riemannian warped product of constant sectional curvature. Generalizing the above results, under a restriction on the sectional curvature or the Ricci curvature tensor of the fiber of a warped product, we also prove some new rigidity theorems in semi-Riemannian warped products. Our main results extend some recent Bernstein-type theorems proved in [12, 13, 14].

scholarly journals New Bernstein Type Results in Weighted Warped Products

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ning Zhang
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Warped Products ◽  
Bernstein Type ◽  
Weighted Mean ◽  
Curvature Equation ◽  
Uniqueness Results ◽  
Mean Curvature Equation ◽  
Weighted Mean Curvature ◽  
Entire Graphs

In this paper, we obtain new parametric uniqueness results for complete constant weighted mean curvature hypersurfaces under suitable geometric assumptions in weighted warped products. Furthermore, we also prove very general Bernstein type results for the constant mean curvature equation for entire graphs in these ambient spaces.

scholarly journals On Bernstein-Type Theorems in Semi-Riemannian Warped Products

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Mean Curvature ◽  
Warped Products ◽  
Bernstein Type ◽  
Complete Spacelike Hypersurfaces ◽  
Spacelike Hypersurfaces ◽  
The Mean

Complete spacelike hypersurfaces immersed in semi-Riemannian warped products are investigated. By using a technique according to Yau (1976) and a reasonable restriction on the mean curvature of the hypersurfaces, we obtain some new Bernstein-type theorems which extend some known results proved by Camargo et al. (2011) and Colares and Lima (2012).

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.

scholarly journals Constant Mean Curvature Spacelike Surfaces in Lorentzian Warped Products

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Juan A. Aledo ◽  
Rafael M. Rubio
Keyword(s):  
Mean Curvature ◽  
Warped Product ◽  
Constant Mean Curvature ◽  
State Of The Art ◽  
The State ◽  
Warped Products ◽  
Type Result ◽  
Bernstein Type ◽  
Spacelike Surfaces ◽  
Lorentzian Warped Product

We characterize the spacelike slices of a Lorentzian warped product as the only constant mean curvature spacelike surfaces under suitable geometrical and physical assumptions. As a consequence of our study, we derive a Bernstein-type result which widely improves and extends the state-of-the-art results in this setting.

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.

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