Conformal mapping from the half-plane onto a circular polygon with cusps

I. A. Kolesnikov

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2021), pp. 11-24.

Résumé

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.

Détail

Keywords: conformal mapping, circular-arc polygon, Schwarz equation, Loewner equation, Kufarev's method.

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