Foliations of globally hyperbolic spacetimes by CMC hypersurfaces

We announce the following result: every maximal globally hyperbolic <f>3</f>-dimensional spacetime with compact Cauchy surface, and with nonpositive constant curvature admits a unique time function whose fibers are constant mean curvature surfaces. We discuss the extension of this result in higher dimensions. To cite this article: T. Barbot et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]