RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE

Title & Authors
RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE
De Lima, Henrique Fernandes;

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 $\small{(n+1)}$-dimensional hyperbolic space $\small{\mathbb{H}^{n+1}}$. In our approach, we explore the existence of a natural duality between $\small{\mathbb{H}^{n+1}}$ and the half $\small{\mathcal{H}^{n+1}}$ of the de Sitter space $\small{\mathbb{S}_1^{n+1}}$, 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
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