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Seminar on Complex Analysis (Gonchar Seminar)
October 27, 2014 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
 


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

V. M. Keselman

Moscow State Industrial University

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Abstract: 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.

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