The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type

We prove that the maximal isoperimetric function on a Riemannian manifold of conformally hyperbolic type can be reduced to the linear canonical form $P(x)=x$ by a conformal change of the Riemannian metric. In other words, the isoperimetric inequality $P(V(D))\le S(\partial D)$, relating the volume $V(D)$ of a domain $D$ to the area $S(\partial D)$ of its boundary, can be reduced to the form $V(D)\le S(\partial D)$, known for the Lobachevskii hyperbolic space.