On the CMC foliation of future ends of a spacetime

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dc.creatorGerhardt, Claus
dc.date2004-08-16
dc.date2006-07-27
dc.date.accessioned2026-07-07T06:38:43Z
dc.date.available2026-07-07T06:38:43Z
dc.descriptionWe consider spacetimes with compact Cauchy hypersurfaces and with Ricci tensor bounded from below on the set of timelike unit vectors, and prove that the results known for spacetimes satisfying the timelike convergence condition, namely, foliation by CMC hypersurfaces, are also valid in the present situation, if corresponding further assumptions are satisfied. In addition we show that the volume of any sequence of spacelike hypersurfaces, which run into the future singularity, decays to zero provided there exists a time function covering a future end, such that the level hypersurfaces have non-negative mean curvature and decaying volume.
dc.description12 pages, a pdf version can also be retrieved from http://www.math.uni-heidelberg.de/studinfo/gerhardt/foliation2.pdf and bibtex data from http://www.math.uni-heidelberg.de/studinfo/gerhardt/bibtexcgfoliation2.html, v2: the result of Lemma 2.1 improved, Theorem 0.3 removed, because it is already known, v3: Minor changes, section numbering starts with 1
dc.identifierhttps://arxiv.org/abs/math/0408197
dc.identifierhttp://arxiv.org/abs/math/0408197
dc.identifierPacific J. Math. 226, 297--308 (2006)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100837
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.titleOn the CMC foliation of future ends of a spacetime
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