  We consider pointed Lorentzian manifolds and construct "canonical" foliations
by constant mean curvature (CMC) hypersurfaces. Our result assumes a uniform
bound on the local sup-norm of the curvature of the manifold and on its local
injectivity radius, only. The prescribed curvature problem under consideration
is a nonlinear elliptic equation whose coefficients have limited regularity.
The CMC foliation allows us to introduce CMC-harmonic coordinates, in which the
coefficients of the Lorentzian metric have optimal regularity.
