We solve the problem of constructing a conformal mapping from the upper half-plane onto a circular polygon with cusps (\(2\pi\) angles). We determine preimages of the polygon vertices and accessory parameters using the generalization of P.P. Kufarev's method of finding parameters in the Schwartz–Christoffel integral. The method is based on the chordal Loewner equation. The problem of finding the parameters of the mapping of the half-plane 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 the half-plane onto a quadrilateral with zero angles.

我们解决了构建从上半平面到具有尖角（\（2\pi\）角）的圆形多边形的共形映射的问题。我们使用 PP Kufarev 在 Schwartz-Christoffel 积分中寻找参数的方法的推广来确定多边形顶点和附属参数的原像。该方法基于弦乐 Loewner 方程。BG Baybarin 和作者早先通过 PP Kufarev 的方法研究了将半平面映射到具有非零和\(2\pi\)角度的多边形的映射参数的问题。我们给出了一个从半平面到零角四边形的映射的例子。