Spacelike hypersurfaces with constant mean curvature in the steady state space

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dc.creatorAlbujer, Alma L.
dc.creatorAlias, Luis J.
dc.date2007-09-27
dc.date2008-02-05
dc.date.accessioned2026-07-07T12:41:53Z
dc.date.available2026-07-07T12:41:53Z
dc.descriptionWe 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.
dc.descriptionFirst version (May 2007). Final version (February 2008). To appear in Proceedings of the A.M.S
dc.identifierhttps://arxiv.org/abs/0709.4398
dc.identifierhttp://arxiv.org/abs/0709.4398
dc.identifierProceedings of the American Mathematical Society 137 (2009), 711--721
dc.identifierdoi:10.1090/S0002-9939-08-09546-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219895
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C42, 53C50
dc.titleSpacelike hypersurfaces with constant mean curvature in the steady state space
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