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The problem of product of conformal radii of nonoverlapping domains

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Abstract

Let a1, a2, a3, b be distinct points in

and let D be the family of all triples of nonoverlapping domains D1, D2, D3 in

\ {b} such that ak∈ Dk, k=1,2,3. For this family we consider the problem on the maximum of the functional I=R1R2R3, where Rk=R(Dk, ak) is the conformal radius of Dk with respect to ak. Geometrical properties of the extremal triple of domains are described. We prove that the maximum of I monotonically depends on the position of the point b and find the maximum in some special cases

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Authors
  1. V. O. Kuznetsov
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Additional information

Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 114–128

Translated by N. Yu. Netsvetaev

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Kuznetsov, V.O. The problem of product of conformal radii of nonoverlapping domains. J Math Sci 83, 762–771 (1997). https://doi.org/10.1007/BF02439203

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  • DOI: https://doi.org/10.1007/BF02439203

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