Mathematics – Mathematical Physics
Scientific paper
Oct 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cmaph..54..279g&link_type=abstract
Communications in Mathematical Physics, Volume 54, Issue 3, pp.279-282
Mathematics
Mathematical Physics
12
Scientific paper
The foliations under discussion are of two different types, although in each case the leaves are C 2 spacelike hypersurfaces of constant mean curvature. For manifolds, such as that of the Friedmann universe with closed spatial sections, which are topologically I× S 3, I an open interval, the leaves will be spacelike hypersurfaces without boundary and the foliation will fill the manifold. In the case of the domain of dependence of a spacelike hypersurface, S, with boundary B, the leaves will be spacelike hypersurfaces with boundary, B, and the foliation will fill D( S). It is shown that a local energy condition ensures that the constant mean curvature increases monotonically with time through such foliations and that, in the case of a foliation whose leaves are spacelike hypersurfaces without boundary in a manifold where this energy condition is satisfied globally, the foliation is unique.
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