For a complete noncompact Riemannian manifold with smoothly bounded geometry, we prove the existence of isoperimetric regions in a larger space obtained by adding finitely many limit manifolds at infinity. As one of many possible applications, we extend properties of the isoperimetric profile from compact manifolds to such noncompact manifolds.
Stefano Nardulli. "Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile." Asian J. Math. 18 (1) 1 - 28, January 2014.