Spacelike Hypersurfaces with Constant Mean Curvature in the Steady State Space

In this paper we obtain height estimates concerning to a compact spacelike hypersurface Sigma(n) immersed with constant mean curvature H in the Steady State space Hn+1, when its boundary is contained into some hyperplane of this spacetime. As a first application of these results, when Sigma(n) has spherical boundary, we establish relations between its height and the radius of its boundary. Moreover, under a certain restriction on the Gauss map of E-n, we obtain a sharp estimate for H. Finally, we also apply our estimates to describe the end of a complete spacelike hypersurface and to get theorems of characterization concerning to spacelike hyperplancs in Hn+1.