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 Ricg ≥ (n− 1)k0g and being locally asymptotic to the simply connected space form of constant sectional curvature k0; moreover in case k0 = 0 we show that the isoperimetric regions are indecomposable. We also discuss some physically and geometrically relevant examples. Finally, under assumptions on the scalar curvature we prove existence of isoperimetric regions of small volume.