  We study the isoperimetric structure of Riemannian manifolds that are
asymptotic to cones with non-negative Ricci curvature. Specifically, we
generalize to this setting the seminal results of G. Huisken and S.-T. Yau on
the existence of a canonical foliation by volume preserving stable constant
mean curvature surfaces at infinity of asymptotically flat manifolds as well as
the results of the second-named author with S. Brendle and J. Metzger on the
isoperimetric structure of asymptotically flat manifolds. We also include an
observation on the isoperimetric cone angle of such manifolds. This result is a
natural analogue of the positive mass theorem in this setting.
