# The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type

@article{Zorich2001TheII, title={The Isoperimetric Inequality on Manifolds of Conformally Hyperbolic Type}, author={Vladimir A. Zorich and Vladimir Mikhailovich Kesel'man}, journal={Functional Analysis and Its Applications}, year={2001}, volume={35}, pages={90-99} }

AbstractWe 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
$$P\left( {V\left( D \right)} \right) \leqslant {\text{S}}\left( {\partial {\text{D}}} \right)$$
, relating the volume V(D) of a domain D to the area
$${\text{S}}\left( {\partial {\text{D}}} \right)$$
of its boundary, can be reduced to… CONTINUE READING