RIGIDITY THEOREMS IN THE HYPERBOLIC SPACE

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 Hn+1. In our approach, we explore the existence of a natural duality between Hn+1 and the half Hn+1 of the de Sitter space S-1(n+1), which models the so-called steady state space.