Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions

We prove existence of isoperimetric regions for every volume in non-compact Riemannian n-manifolds (M, g), n >= 2, having Ricci curvature Ric(g) >= (n - 1)k(0g) and being C-0-locally asymptotic to the simply connected space form of constant sectional curvature k(0) <= 0; moreover in case k(0) = 0 we show that the isoperimetric regions are indecomposable. Our results apply to a large class of physically and geometrically relevant examples: Eguchi-Hanson metric and more generally ALE gravitational instantons, asymptotically hyperbolic Einstein manifolds, Bryant type solitons, etc. Finally, under assumptions on the scalar curvature, we prove existence of isoperimetric regions of small volume.