Geodesic
Unique determination of~conformal type for~domains.~III
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 104-111.

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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. 
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A. P. Kopylov. Unique determination of~conformal type for~domains.~III. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 104-111. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a39/

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