Geodesic
Conformal mapping from the half-plane onto a circular polygon with cusps
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 11-24

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

The paper solves the problem of constructing a conformal mapping from the upper half-plane onto a circular-arc polygon with zero angles ($2\pi$ angles). We determine preimages of the polygon vertices and accessory parameters using the generalized of P.P. Kufarev's method of finding parameters in the Christoffel-Schwartz integral. The method is based on the chordal Loewner equation. The problem of finding the parameters of the mapping onto a polygon with angles other than zero and $2\pi$ was investigated earlier by B.G. Baybarin and the author by P.P. Kufarev's method. We give an example of finding the mapping from a half-plane onto a quadrilateral with zero angles.
Keywords: conformal mapping, circular-arc polygon, Schwarz equation, Loewner equation, Kufarev's method. 
@article{IVM_2021_6_a1,
     author = {I. A. Kolesnikov},
     title = {Conformal mapping from the half-plane onto a circular polygon with cusps},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--24},
     publisher = {mathdoc},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_6_a1/}
}
TY  - JOUR
AU  - I. A. Kolesnikov
TI  - Conformal mapping from the half-plane onto a circular polygon with cusps
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 11
EP  - 24
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_6_a1/
LA  - ru
ID  - IVM_2021_6_a1
ER  - 
%0 Journal Article
%A I. A. Kolesnikov
%T Conformal mapping from the half-plane onto a circular polygon with cusps
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 11-24
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_6_a1/
%G ru
%F IVM_2021_6_a1
I. A. Kolesnikov. Conformal mapping from the half-plane onto a circular polygon with cusps. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 11-24. http://geodesic.mathdoc.fr/item/IVM_2021_6_a1/