Geodesic
The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type
Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 12-23

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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. 
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     author = {V. A. Zorich and V. M. Kesel'man},
     title = {The {Isoperimetric} {Inequality} on {Manifolds} of {Conformally} {Hyperbolic} {Type}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {12--23},
     publisher = {mathdoc},
     volume = {35},
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V. A. Zorich; V. M. Kesel'man. The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type. Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 12-23. http://geodesic.mathdoc.fr/item/FAA_2001_35_2_a1/