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

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.