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We study the isoperimetric structure of Riemannian manifolds that areasymptotic to cones with non-negative Ricci curvature. Specifically, wegeneralize to this setting the seminal results of G. Huisken and S.-T. Yau onthe existence of a canonical foliation by volume preserving stable constantmean curvature surfaces at infinity of asymptotically flat manifolds as well asthe results of the second-named author with S. Brendle and J. Metzger on theisoperimetric structure of asymptotically flat manifolds. We also include anobservation on the isoperimetric cone angle of such manifolds. This result is anatural analogue of the positive mass theorem in this setting.

Isoperimetric structure of asymptotically conical manifolds