Geodesic
On the search for parameters of a conformal mapping from a half-plane to a circular polygon
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 56-68

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

The problem of constructing a conformal mapping from a half-plane to a circular polygon is considered. The preimages of the vertices of the polygon and accessory parameters are determined by the generalized method of P. P. Kufarev for determining the parameters in the Christoffel–Schwarz integral. The method is based on the Loewner equation with boundary normalization. The problem of constructing a mapping from a half-plane onto the exterior of a polygon with a boundary consisting of straight-line segments is solved separately. Examples of mappings whose parameters are found by the Kufarev method are given.
Keywords: conformal mapping, circular polygon, Schwarz equation, Kufarev method. 
@article{INTO_2020_175_a5,
     author = {I. A. Kolesnikov},
     title = {On the search for parameters of a conformal mapping from a half-plane to a circular polygon},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {56--68},
     publisher = {mathdoc},
     volume = {175},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_175_a5/}
}
TY  - JOUR
AU  - I. A. Kolesnikov
TI  - On the search for parameters of a conformal mapping from a half-plane to a circular polygon
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 56
EP  - 68
VL  - 175
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_175_a5/
LA  - ru
ID  - INTO_2020_175_a5
ER  - 
%0 Journal Article
%A I. A. Kolesnikov
%T On the search for parameters of a conformal mapping from a half-plane to a circular polygon
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 56-68
%V 175
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_175_a5/
%G ru
%F INTO_2020_175_a5
I. A. Kolesnikov. On the search for parameters of a conformal mapping from a half-plane to a circular polygon. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 56-68. http://geodesic.mathdoc.fr/item/INTO_2020_175_a5/