On the foliation of space-time by constant mean curvature hypersurfaces

Abstract

We prove that the mean curvature $\tau$ of the slices given by a constant mean curvature foliation can be used as a time function, i.e. $\tau$ is smooth with non-vanishing gradient.

7 pages, amslatex, The paper is from 1999. A pdf version of the paper can be retrieved from http://www.math.uni-heidelberg.de/studinfo/gerhardt/Foliation.pdf and bibtex data from http://www.math.uni-heidelberg.de/studinfo/gerhardt/bibtexcg99.html

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• Cosmological Measures without Volume Weighting
• Hypersurfaces of prescribed scalar curvature in Lorentzian manifolds