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Siberian Journal of Pure and Applied Mathematics, 2017, Volume 17, Issue 2, Pages 13–20
DOI: https://doi.org/10.17377/PAM.2017.17.202 (Mi vngu435) 		 
On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components

A. P. Kopylovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
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DOI: https://doi.org/10.17377/PAM.2017.17.202
Abstract: 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 the conformal moduli (extremal lengths) of the pairs of boundary components of the domain under consideration in the case where its connectedness is at most $3$.
Keywords: finitely-connected plane domain, relative conformal modulus of a pair of boundary components of the domain, Teichmüller and Grötzsch extremal domains.
Received: 09.08.2016
English version:
Journal of Mathematical Sciences, 2018, Volume 231, Issue 2, Pages 181–188
DOI: https://doi.org/10.1007/s10958-018-3814-0
Document Type: Article
UDC: 514.772.35
Language: Russian
Citation: A. P. Kopylov, “On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components”, Sib. J. Pure and Appl. Math., 17:2 (2017), 13–20; J. Math. Sci., 231:2 (2018), 181–188
Citation in format AMSBIB
\Bibitem{Kop17}
\by A.~P.~Kopylov
\paper On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components
\jour Sib. J. Pure and Appl. Math.
\yr 2017
\vol 17
\issue 2
\pages 13--20
\mathnet{http://mi.mathnet.ru/vngu435}
\crossref{https://doi.org/10.17377/PAM.2017.17.202}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 231
\issue 2
\pages 181--188
\crossref{https://doi.org/10.1007/s10958-018-3814-0}
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