Bulletin of the
Korean Mathematical Society BKMS

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