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Generalized existence of isoperimetric regions in non-compact Riemannian manifolds and applications to the isoperimetric profile
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.