  It is shown that in a class of maximal globally hyperbolic spacetimes
admitting two local Killing vectors, the past (defined with respect to an
appropriate time orientation) of any compact constant mean curvature
hypersurface can be covered by a foliation of compact constant mean curvature
hypersurfaces. Moreover, the mean curvature of the leaves of this foliation
takes on arbitrarily negative values and so the initial singularity in these
spacetimes is a crushing singularity. The simplest examples occur when the
spatial topology is that of a torus, with the standard global Killing vectors,
but more exotic topologies are also covered. In the course of the proof it is
shown that in this class of spacetimes a kind of positive mass theorem holds.
The symmetry singles out a compact surface passing through any given point of
spacetime and the Hawking mass of any such surface is non-negative. If the
Hawking mass of any one of these surfaces is zero then the entire spacetime is
flat.
