The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type

V. A. Zorich ; V. M. Kesel'man

Funkcionalʹnyj analiz i ego priloženiâ, Tome 35 (2001) no. 2, pp. 12-23.

Résumé

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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