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On unique determination of 3-connected plane domains by relative conformal moduli of pairs of boundary components

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An Erratum to this article was published on 01 November 2016

Abstract

The boundary values of conformal mappings of plane finitely connected domains are studied. A complete description of the boundary values of such mappings in terms of the moduli (extremal lengths) of pairs of boundary components of domains is obtained in the case where the number of boundary components is not larger than three.

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References

  1. B. Fuglede, Acta Math. 98, 171–219 (1957).

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  2. J. Väisälä, Lectures on n-Dimensional Quasiconformal Mappings (Springer-Verlag, Berlin, 1973).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

    A. P. Kopylov

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. P. Kopylov

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

Additional information

Original Russian Text © A.P. Kopylov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 468, No. 1, pp. 137–138.

An erratum to this article is available at http://dx.doi.org/10.1134/S1064562416060120.

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Kopylov, A.P. On unique determination of 3-connected plane domains by relative conformal moduli of pairs of boundary components. Dokl. Math. 93, 262–263 (2016). https://doi.org/10.1134/S1064562416030054

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  • DOI: https://doi.org/10.1134/S1064562416030054

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