Global prescribed mean curvature foliations in cosmological space–times. I

Abstract

This work investigates some global questions about cosmological space–times with two-dimensional spherical, plane, and hyperbolic symmetry containing “well-behaved” matter. The result is that these space–times admit a global foliation by prescribed mean curvature surfaces, which extends at least toward a crushing singularity. The time function of the foliation is geometrically defined and unique up to the choice of an initial Cauchy surface. This work generalizes a similar analysis on constant mean curvature foliations and avoids the topological obstructions arising from the existence problem.