Spacelike hypersurfaces with constant mean curvature in the steady state space

Details Spacelike hypersurfaces with constant mean curvature in the steady state space Spacelike hypersurfaces with constant mean curvature in the steady state space

2007-09-27

arxiv.org/abs/0709.4398v2

Proceedings of the American Mathematical Society 137 (2009), 711--721

Mathematics

Differential Geometry

First version (May 2007). Final version (February 2008). To appear in Proceedings of the A.M.S

Scientific paper

10.1090/S0002-9939-08-09546-4

We consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that if the hypersurface is bounded away from the infinity of the ambient space, then the mean curvature must be H=1. Moreover, in the 2-dimensional case we obtain that the only complete spacelike surfaces with constant mean curvature which are bounded away from the infinity are the totally umbilical flat surfaces. We also derive some other consequences for hypersurfaces which are bounded away from the future infinity. Finally, using an isometrically equivalent model for the steady state space, we extend our results to a wider family of spacetimes.

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