Conformal type and isoperimetric dimension of Riemannian manifolds

The notion of conformal isoperimetric dimension is introduced. For Riemannian manifolds, connections between its conformal isoperimetric dimension and its conformal type are established. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 379–385, March, 1998. The authors are greatly indebted to N. A. Zorich for her help in preparing the computer version of this paper. This research was partially supported by the Russian Foundation for Basic Research under grants No. 96-01-01218 and No. 96-01-00901.