Hipersuperfícies tipo-espaço completas com curvatura média constante imersas no Steady State Space.

Abstract

In this work we study complete space-like hypersurfaces with constant mean curvature in the open region of de Sitter space, called the Steady State Space. First established suitable formulas for the Laplacian of a height function and of a suport function related to these hypersurfaces. Then, considering hypotheses appropriate on the mean curvature and growth of height functions we obtain necessary conditions for the existence of such hypersurfaces. In two-dimensional case, we set and show results-Bernstein type. Furthermore, we show that if the hypersurface is between two slices then its mean curvature is equal to one. We also obtain other consequences for hypersurfaces are below a slice. Finally, we extend one of our results to a certain space generalized Robertson-Walker.