JOURNAL BROWSE
Search
Advanced SearchSearch Tips
RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE
De Lima, Henrique Fernandes;
  PDF(new window)
 Abstract
As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the -dimensional hyperbolic space . In our approach, we explore the existence of a natural duality between and the half of the de Sitter space , which models the so-called steady state space.
 Keywords
hyperbolic space;complete hypersurfaces;mean curvature;Gauss map;
 Language
English
 Cited by
1.
On Bernstein-Type Theorems in Semi-Riemannian Warped Products, Advances in Mathematical Physics, 2013, 2013, 1  crossref(new windwow)
 References
1.
L. J. Alias and M. Dajczer, Uniqueness of constant mean curvature surfaces properly immersed in a slab, Comment. Math. Helv. 81 (2006), no. 3, 653-663.

2.
F. E. C. Camargo, A. Caminha, and H. F. de Lima, Bernstein-type Theorems in Semi-Riemannian Warped Products, Proc. Amer. Math. Soc. 139 (2011), no. 5, 1841-1850. crossref(new window)

3.
A. Caminha and H. F. de Lima, Complete vertical graphs with constant mean curvature in semi-Riemannian warped products, Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 1, 91-105.

4.
A. Huber, On subharmonic functions and differential geometry in the large, Comment. Math. Helv. 32 (1957), 13-72.

5.
H. F. de Lima, Spacelike hypersurfaces with constant higher order mean curvature in de Sitter space, J. Geom. Phys. 57 (2007), no. 3, 967-975. crossref(new window)

6.
R. Lopez and S. Montiel, Existence of constant mean curvature graphs in hyperbolic space, Calc. Var. Partial Differential Equations 8 (1999), no. 2, 177-190. crossref(new window)

7.
S. Montiel, Complete non-compact spacelike hypersurfaces of constant mean curvature in de Sitter spaces, J. Math. Soc. Japan 55 (2003), no. 4, 915-938. crossref(new window)

8.
S. Montiel, Unicity of constant mean curvature hypersurfaces in some Riemannian manifolds, Indiana Univ. Math. J. 48 (1999), no. 2, 711-748.

9.
S. Montiel, Uniqueness of spacelike hypersurfaces of constant mean curvature in foliated spacetimes, Math. Ann. 314 (1999), no. 3, 529-553. crossref(new window)

10.
S. Montiel, An integral inequality for compact spacelike hypersurfaces in De Sitter space and applications to the case of constant mean curvature, Indiana Univ. Math. J. 37 (1988), no. 4, 909-917. crossref(new window)

11.
H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. crossref(new window)

12.
S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. crossref(new window)

13.
S. T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry, Indiana Univ. Math. J. 25 (1976), no. 7, 659-670. crossref(new window)