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