  We prove the existence and uniqueness of constant mean curvature foliations
for initial data sets which are asymptotically flat satisfying the
Regge-Teitelboim condition near infinity. It is known that the (Hamiltonian)
center of mass is well-defined for manifolds satisfying this condition. We also
show that the foliation is asymptotically concentric, and its geometric center
is the center of mass. The construction of the foliation generalizes the
results of Huisken-Yau, Ye, and Metzger, where strongly asymptotically flat
manifolds and their small perturbations were studied.
