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

Foliations by Stable Spheres with Constant Mean Curvature for Isolated Systems with General Asymptotics