CONSTANT MEAN-CURVATURE FOLIATIONS IN COSMOLOGICAL SPACETIMES

Foliations by constant mean curvature hypersurfaces provide a possibil ity of defining a preferred time coordinate in general relativity. In the following various conjectures are made about the existence of foli ations of this kind in spacetimes satisfying the strong energy conditi on and possessing compact Cauchy hypersurfaces. Recent progress on pro ving these conjectures under supplementary assumptions is reviewed. Th e method of proof used is explained and the prospects for generalizing it discussed. The relations of these questions to cosmic censorship a nd the closed universe recollapse conjecture are pointed out.