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Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components

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We study the boundary values of conformal mappings of plane finitely connected domains. We present a complete exposition of a theorem giving an exhaustive description of the boundary values of such mappings in terms of conformal moduli (extremal lengths) of pairs of boundary components of a domain of connectedness at most 3. Bibliography: 12 titles.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk, 630090, Russia

    A. P. Kopylov

  2. Novosibirsk State University, 1, Pirogova St., Novosibirsk, 630090, Russia

    A. P. Kopylov

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  1. A. P. Kopylov
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Correspondence to A. P. Kopylov.

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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 17, No. 2, 2017, pp. 13-20.

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Kopylov, A.P. Unique Determination of 3-Connected Plane Domains by Relative Conformal Moduli of Pairs of Boundary Components. J Math Sci 231, 181–188 (2018). https://doi.org/10.1007/s10958-018-3814-0

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  • DOI: https://doi.org/10.1007/s10958-018-3814-0

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