The isoperimetric inequality on conformally parabolic manifolds

For non-compact Riemannian manifolds without boundary the following conjecture is proved: on a Riemannian manifold of conformally parabolic type, after a conformal change of the metric the isoperimetric function (responsible for the isoperimetric inequality) can be transformed into the same form as in the case of the Euclidean space of the corresponding dimension.
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