It is shown that on an arbitrary non-compact Riemannian manifold of conformally hyperbolic type the isoperimetric inequality can be taken by a conformal change of the metric to the same canonical linear form as in the case of the standard hyperbolic Lobachevskii space. Both the absolute isoperimetric inequality and the relative one (for manifolds with boundary) are obtained.This work develops the results and methods of a joint paper with Zorich, in which the absolute isoperimetric inequality was obtained under a certain additional condition; the resulting statements axe definitive in a certain sense.
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