Bull. Korean Math. Soc. 2013; 50(1): 97-103
Printed January 31, 2013
https://doi.org/10.4134/BKMS.2013.50.1.97
Copyright © The Korean Mathematical Society.
Henrique Fernandes de Lima
Universidade Federal de Campina Grande
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
MSC numbers: Primary 53C42; Secondary 53B30, 53C50
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