[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.1.097

RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE

De Lima, Henrique Fernandes (Departamento de Matematica e Estatistica Universidade Federal de Campina Grande)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.1, 2013 , pp. 97-103 More about this Journal

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

Keywords

hyperbolic space; complete hypersurfaces; mean curvature; Gauss map;

Citations & Related Records

Reference

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