  In this paper we prove the existence of isoperimetric regions of any volume
in Riemannian manifolds with Ricci bounded below and with a mild assumption at
infinity, that is Gromov-Hausdorff asymptoticity to simply connected models of
constant sectional curvature. The previous result is a consequence of a general
structure theorem for perimeter-minimizing sequences of sets of fixed volume on
noncollapsed Riemannian manifolds with a lower bound on the Ricci curvature. We
show that, without assuming any further hypotheses on the asymptotic geometry,
all the mass and the perimeter lost at infinity, if any, are recovered by at
most countably many isoperimetric regions sitting in some Gromov-Hausdorff
limits at infinity. The Gromov-Hausdorff asymptotic analysis conducted allows
us to provide, in low dimensions, a result of nonexistence of isoperimetric
regions in Cartan-Hadamard manifolds that are Gromov-Hausdorff asymptotic to
the Euclidean space. While studying the isoperimetric problem in the smooth
setting, the nonsmooth geometry naturally emerges, and thus our treatment
combines techniques from both the theories.
