  We prove that any regular domain in Minkowski space is uniquely foliated by
spacelike constant mean curvature (CMC) hypersurfaces. This completes the
classification of entire spacelike CMC hypersurfaces in Minkowski space
initiated by Choi and Treibergs. As an application, we prove that any entire
surface of constant Gaussian curvature in 2+1 dimensions is isometric to a
straight convex domain in the hyperbolic plane.
