Continuity and differentiability properties of the isoperimetric profile in complete noncompact Riemannian manifolds with bounded geometry

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For a complete noncompact connected Riemannian manifold with bounded geometry Mⁿ, we prove that the isoperimetric profile function Iₘₙ is continuous. Here for bounded geometry we mean that M have Ricci curvature bounded below and volume of balls of radius 1, uniformly bounded below with respect to its centers. Then under an extra hypothesis on the geometry of M, we apply this result to prove some differentiability property of Iₘ and a differential inequality satisfied by Iₘ, extending in this way well known results for compact manifolds, to this class of noncompact complete Riemannian manifolds with bounded geometry.