Conformal capacity, conformal type and isoperimetric function of a Riemannian manifold

We will discuss:
– How to use the conformal capacity of non-compact Riemannian manifold to split such manifolds in conformally invariant manner into two types: conformally parabolic and conformally hyperbolic types.
– How to reduce the isoperimetric inequality on a manifold to one of the two normal forms, depending on the conformal type of a manifold, by conformal change of its original metric.
Finally, in terms of isoperimetric inequality we present a criterion of conformal type of a non-compact Riemannian manifold.
All the necessary definitions, tracing back to the geometric function theory and geometry, will be given in the talk.