  We construct 2-surfaces of prescribed mean curvature in 3-manifolds carrying
asymptotically flat initial data for an isolated gravitating sysqtem with
rather general decay conditions. The surfaces in question form a regular
foliation of the asymptotic region of such a manifold. We recover physically
relevant data, especially the ADM-momentum, from the geometry of the foliation.
  For a given set of data (M,g,K), with a three dimensional manifold M, its
Riemannian metric g, and the second fundamental form K in the surrounding four
dimensional Lorentz space time manifold, the equation we solve is H+P=const or
H-P=const. Here H is the mean curvature, and P = tr K is the 2-trace of K along
the solution surface. This is a degenerate elliptic equation for the position
of the surface. It prescribes the mean curvature anisotropically, since P
depends on the direction of the normal.
