Alexander Kuznetsov

On a problem of Avhadiev

(Lobachevskii Journal of Mathematics, Volume XVI)

In this paper we consider a lower estimate for the ratio I(Ω) of the conformal moment of a simple connected domain Ω in the complex plane to the moment of inertia of this domain about its boundary. Related functionals depending on a simple connected domain Ω and two points w1,w2 ∈ Ω with fixed hyperbolical distance between them are estimated. As a consequence a nontrivial lower estimate for I(Ω) is obtained.



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