2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67264We prove that the mean curvature $τ$ of the slices given by a constant mean curvature foliation can be used as a time function, i.e. $τ$ 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.htmlDifferential GeometryGeneral Relativity and Quantum Cosmology35J60, 53C21, 53C44, 53C50, 58J05text