Spacelike hypersurfaces with constant mean curvature in the steady state space

Abstract

In this paper we obtain height estimates concerning to a compact spacelike hypersurface Sn immersedwith 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 Sn 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 Sn, 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 hyperplanes in Hn+1.