Canonical Form for the Isoperimetric Inequality on Manifolds of Conformally211 Hyperbolic Type

摘要

The authors prove that on any Riemannian manifold of conformally hyperbolic type211u001ethe maximal isoperimetric function can be reduced to the linear canonical form 211u001eP(x) = x by means of a conformal change of the initial Riemmanian metric. In 211u001eother words, the isoperimetric inequality relating the volume of a domain and the 211u001earea of its boundary can be reduced to the form as in Lobachevski hyperbolic 211u001espace.