Abstract We consider Mityuk's function and radius which have been proposed in [15] as generalizations of the reduced modulus and conformal radius to the cases of multiply connected domains. We present a numerical method to compute Mityuk's function and radius for canonical domains that consist of the unit disk with circular/radial slits. Our method is based on the boundary integral equation with the generalized Neumann kernel. Special attention is given to the validation of the theoretical results on the existence of critical points and the boundary behavior of Mityuk's radius.

中文翻译：

---

圆形/径向狭缝域的 Mityuk 函数和半径的数值计算

摘要 我们将 [15] 中提出的 Mityuk 函数和半径视为减少模数和共形半径对多连接域情况的推广。我们提出了一种数值方法来计算由具有圆形/径向狭缝的单位圆盘组成的规范域的 Mityuk 函数和半径。我们的方法基于具有广义 Neumann 核的边界积分方程。特别注意对临界点的存在和 Mityuk 半径的边界行为的理论结果的验证。