Geodesic
Unique determination of conformal type for domains. III
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 104-111 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SEMR_2021_18_1_a39,
     author = {A. P. Kopylov},
     title = {Unique determination of~conformal type {for~domains.~III}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {104--111},
     year = {2021},
     volume = {18},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a39/}
}
TY  - JOUR
AU  - A. P. Kopylov
TI  - Unique determination of conformal type for domains. III
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2021
SP  - 104
EP  - 111
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a39/
LA  - en
ID  - SEMR_2021_18_1_a39
ER  - 
%0 Journal Article
%A A. P. Kopylov
%T Unique determination of conformal type for domains. III
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2021
%P 104-111
%V 18
%N 1
%U http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a39/
%G en
%F SEMR_2021_18_1_a39
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/

[1] A.P. Kopylov, “Unique determination of conformal type for domains”, Sib. Elektron. Mat. Izv., 16 (2019), 692–708 | Zbl

[2] A.P. Kopylov, “Unique determination of conformal type for domains. II”, Sib. Elektron. Mat. Izv., 16 (2019), 1205–1214 | Zbl

[3] B. Fuglede, “Extremal length and functional completion”, Acta Math., 98 (1957), 171–219 | Zbl

[4] J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Springer, Berlin–Heidelberg–New York, 1973 | Zbl

[5] A.P. Kopylov, “On unique determination of 3-connected plane domains by relative conformal moduli of pairs of boundary components”, Dokl. Math., 93:3 (2016), 262–263 | Zbl

[6] G.M. Goluzin, Geometric theory of functions of a complex variable, Translations of Mathematical Monographs, 26, AMS, Providence, RI, 1969 | Zbl

[7] O. Teichmüller, “Untersuchungen über konforme und quasikonforme Abbildung”, Deutsche Math., 3 (1938), 621–678 | Zbl

[8] F.W. Gehring, “Lipschitz mappings and the $p$-capacity of rings in $n$-space”, Annals of Mathematics Studies, 66 (1971), 175–193 | Zbl

[9] F.W. Gehring, “Rings and quasiconformal mappings in space”, Trans. Am. Math. Soc., 103 (1962), 353–393 | Zbl

[10] F.W. Gehring, J. Väisälä, “The coefficients of quasiconformality of domains in space”, Acta Math., 114:1-2 (1965), 1–70 | Zbl