  We describe explicitly the large volume isoperimetric regions of a natural
class of asymptotically flat manifolds, in any dimension. These isoperimetric
regions detect the mass and the center of mass of such manifolds when viewed as
initial data sets for the Einstein equations in general relativity. Using the
positivity of the isoperimetric mass established by G. Huisken we prove an
existence result for large isoperimetric regions in general asymptotically flat
three manifolds with non-negative scalar curvature.
