Bernstein type result for constant mean curvature hypersurface

2008 ◽  
Vol 3 (3) ◽  
pp. 345-353
Author(s):  
Huaqiao Liu ◽  
Qingyu Meng
Keyword(s):  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Type Result ◽  
Bernstein Type ◽  
Constant Mean Curvature Hypersurface ◽  
Curvature Hypersurface

Symmetry-Breaking for Immersed Constant Mean Curvature Hypersurfaces

2009 ◽  
Vol 9 (2) ◽  
Author(s):  
Mohamed Jleli
Keyword(s):  
Symmetry Breaking ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Jacobi Operator ◽  
Constant Mean Curvature Hypersurfaces ◽  
The Family ◽  
Constant Mean Curvature Hypersurface ◽  
Curvature Hypersurface

AbstractIn this paper we prove the existence of constant mean curvature hypersurfaces which are cylindrically bounded and which bifurcate from the family of immersed constant mean curvature hypersurface of revolution. Based on the study of the spectrum of the Jacobi operator (the linearized mean curvature) about this family, the existence of new branches follows from a bifurcation result of Crandall and Rabinowitz.

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.

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 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 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.

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