The following paragraphs come from Yau's talk in Weihai in the
occasion of the seventieth anniversary of the Chinese Mathematics
Society.\

{sl For surfaces with constant mean curvature, we have the
concept of stability. (Fixing the volume it encloses, the second
variation of area is non-negative.) Making use of my works on
eigenvalues with Peter Li, Christodoulou and I proved that the
Hawking mass of these surfaces is positive. This fact was used by
Huisken and I to prove uniqueness and existence of foliation by
constant mean curvature spheres for a three dimensional
asymptotically flat manifold with positive mass. After ten years,
Tian and Qing reproduced our uniqueness result, but the argument
is basically the same.

This foliation was used by Huisken and Yau to give a canonical coordinate system at infinity. It defines the concept of center of gravity where
important properties for general relativity are found. The most
notable is that total linear momentum is equal to the total mass
multiple with the velocity of the center of mass. One expects to
find good asymptotic properties of the tensors in general
relativity along these canonical surfaces. We hope to find a good
definition of angular momentum based on this concept of center of
gravity so that global inequality like total mass can dominate the
square norm of angular momentum.

In the above theorem of Huisken-Yau, the uniqueness of foliation
is true in a neighborhood of infinity whose size depends on the
choice of both foliations. This is good enough for defining center
of mass which is the key purpose of the foliation. They also
proposed to enlarge the neighborhood for uniqueness of level sets
with constant mean curvature so that it depends only on the choice
of one foliation. While it has some interest, it has little to do
with the above applications in general relativity. This proposal
was observed to be true (Qing-Tian) based basically on the same
argument of Huisken-Yau and a simple integral xxxxula.}\

Note on page 2 of the paper of Qing-Tian
(arXiv:math.DG/0506005 v1 Jun 2005), They claim:\

{sl In this note we show that indeed on an asymptotically flat
3-manifold with positive mass there is a unique foliation of
stable spheres of constant mean curvature near the end.} \

This statement can be found on page 301 of Huisken-Yau (Invent.
Math. {bf 124}(1996), 281-311):\

{sl In this section we will show that the foliation
${M_sigma}$ constructed in Theorem 3.1 and Theorem 4.1 is
unique. In fact, we show that the individual surfaces $M_sigma$
are the only stable constant mean curvature surfaces outside a
small interior region of $N$.}