Spacelike hypersurfaces with constant mean curvature in the steady state space (Q5901030)

The authors obtain height estimates concerning to a compact spacelike hypersurface \(\Sigma^n\) immersed with constant mean curvature \(H\) in the steady state space \({\mathcal H}^{n+1}\), when its boundary is contained into some hyperplane of this spacetime. As a first application of these results, when \(\Sigma^n\) has spherical boundary, they establish relations between its height and the radius of its boundary. Moreover, under a certain restriction on the Gauss map of \(\Sigma^n\), they obtain a sharp estimate for \(H\). Finally, the authors also apply their estimates to describe the end of a complete spacelike hypersurface and to get theorems of characterization concerning to spacelike hyperplanes in \({\mathcal H}^{n+1}\).