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Maximum of a conformal, invariant in the problem of nonoverlapping domains

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Abstract

The paper is devoted to the well-known circle of problems on the maximum of the products of powers of conformal radii of nonoverlapping domains. Let a1, ..., an be distinct points of ℂ and let D1, ..., Dn be a system of simply connected domains in

, pairwise disjoint and such that akεDk, k=1, ..., n. By R(Dkak) we denote the conformal radius of the domain Dk relative to the point ak. One considers the problem on the maximum of the product

in the family of all indicated systems of domains, under the condition that a1, ..., an runs over all systems of distinct points in ℂ (n⩾4) and one finds the geometric characteristic of the extremal configurations of this problem in terms of the associated quadratic differential.

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Authors
  1. S. I. Fedorov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 172–183, 1981.

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Fedorov, S.I. Maximum of a conformal, invariant in the problem of nonoverlapping domains. J Math Sci 25, 1093–1101 (1984). https://doi.org/10.1007/BF01680833

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  • DOI: https://doi.org/10.1007/BF01680833

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