  In 1996, Huisken-Yau showed that every three-dimensional Riemannian manifold
can be uniquely foliated near infinity by stable closed CMC-surfaces if it is
asymptotically equal to the (spatial) Schwarzschild solution and has positive
mass. Their assumptions were later weakened by Metzger, Huang, Eichmair-Metzger
and others. We further generalize these existence results in dimension three by
proving that it is sufficient to assume asymptotic flatness and non-vanishing
mass to conclude the existence and uniqueness of the CMC-foliation and explain
why this seems to be the conceptually optimal result. Furthermore, we
generalize the characterization of the corresponding coordinate CMC-center of
mass by the ADM-center of mass proven previously by Corvino-Wu, Huang,
Eichmair-Metzger and others (under other assumptions).
