Geodesic
On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 13-20

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{VNGU_2017_17_2_a1,
     author = {A. P. Kopylov},
     title = {On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {13--20},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a1/}
}
TY  - JOUR
AU  - A. P. Kopylov
TI  - On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2017
SP  - 13
EP  - 20
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a1/
LA  - ru
ID  - VNGU_2017_17_2_a1
ER  - 
%0 Journal Article
%A A. P. Kopylov
%T On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2017
%P 13-20
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a1/
%G ru
%F VNGU_2017_17_2_a1
A. P. Kopylov. On the unique determination of three-connected plane domain by the relative conformal moduli of the boundary components. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 2, pp. 13-20. http://geodesic.mathdoc.fr/item/VNGU_2017_17_2_a1/