Unique isoperimetric foliations of asymptotically flat manifolds in all dimensions

Michael Eichmair, Jan Metzger

Published 2012-04-26, updated 2013-02-04Version 2

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.