Geodesic
Conformal maps of a region that is geometrically close to a disk
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 116-147 
M. S. Kuznetsova; N. A. Shirokov. Conformal maps of a region that is geometrically close to a disk. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 116-147. http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a7/
@article{ZNSL_2022_512_a7,
     author = {M. S. Kuznetsova and N. A. Shirokov},
     title = {Conformal maps of a region that is geometrically close to a disk},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--147},
     year = {2022},
     volume = {512},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a7/}
}
TY  - JOUR
AU  - M. S. Kuznetsova
AU  - N. A. Shirokov
TI  - Conformal maps of a region that is geometrically close to a disk
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 116
EP  - 147
VL  - 512
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a7/
LA  - ru
ID  - ZNSL_2022_512_a7
ER  - 
%0 Journal Article
%A M. S. Kuznetsova
%A N. A. Shirokov
%T Conformal maps of a region that is geometrically close to a disk
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 116-147
%V 512
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a7/
%G ru
%F ZNSL_2022_512_a7

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $D$ be a Jordan domain differing from the unit disk in a finite number of domains of small diameter, and let $f$ be a conformal mapping of $D$ onto the unit disk. Under some additional assumptions, the deviation of $f$ from the identity mapping is estimated in explicit terms.

[1] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[2] N. A. Shirokov, “Kolichestvennoe utochnenie teoremy Rado”, Zap. nauchn. sem. LOMI, 157, Izd-vo Nauka, Leningrad. otd., L., 1987, 103–112

[3] N. A. Shirokov, “O srednikh stepeni – $2$ proizvodnykh v klasse S”, Algebra i analiz, 28:6 (2016), 189–207

[4] I. I. Privalov, Granichnye svoistv analiticheskikh funktsii, Gos. izd-vo tekhniko-teoreticheskoi literatury, M.–L., 1950 | MR

[5] L. Alfors, Lektsii po kvazikonformnym otobrazheniyam, Per. s angl. V. V. Krivova, Mir, M., 1969

[6] P. P. Belinskii, Obschie svoistva kvazikonformnykh otobrazhenii, Nauka, Novosibirsk, 1974