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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 1, Pages 104–111
DOI: https://doi.org/10.33048/semi.2021.18.009 (Mi semr1350) 		 
Real, complex and functional analysis

Unique determination of conformal type for domains. III

A. P. Kopylovab

a Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.009
Abstract: The article is the third (final) part of a review series entitled “Unique determination of conformal type for domains,” initiated by the author's eponymous paper, published in Sib. Èlektron. Mat. Izv., 16, 692–708 (2019). The main result of the present article is that for $n \le 3$, any $n$-connected plane domain $U$ is uniquely determined by the relative conformal moduli of pairs of boundary components.
Keywords: finitely connected plane domain, relative conformal modulus of pairs of boundary components, Teichmüller and Grötzsch extremal domains.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00661 A
The author was partially supported by the Russian Foundation for Basic Research (Grant 20-01-00661 A (2020-2022)).
Received January 25, 2020, published February 18, 2021
Bibliographic databases:
Document Type: Article
UDC: 514.772.35
MSC: 30C65, 53C24
Language: English
Citation: A. P. Kopylov, “Unique determination of conformal type for domains. III”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 104–111
Citation in format AMSBIB
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\by A.~P.~Kopylov
\paper Unique determination of~conformal type for~domains.~III
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 1
\pages 104--111
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\crossref{https://doi.org/10.33048/semi.2021.18.009}
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