论文标题
平面域上Hurwitz度量的Carathéodory密度
Carathéodory density of the Hurwitz metric on plane domains
论文作者
论文摘要
众所周知，carathéodory度量是对庞加莱度量标准的自然概括，即单位磁盘的双曲线指标。 2016年，D。Minda在复杂平面的任意适当子域中引入了Hurwitz度量标准，他证明，当域仅连接到域时，该度量与双曲线指标相吻合。在本文中，我们定义了一个新的度量标准，该指标从Carathéodory的意义上概括了Hurwitz指标。我们的主要重点是研究与Hurwitz指标相关的各种基本属性。
It is well-known that the Carathéodory metric is a natural generalization of the Poincaré metric, namely, the hyperbolic metric of the unit disk. In 2016, the Hurwitz metric was introduced by D. Minda in arbitrary proper subdomains of the complex plane and he proved that this metric coincides with the hyperbolic metric when the domains are simply connected. In this paper, we define a new metric which generalizes the Hurwitz metric in the sense of Carathéodory. Our main focus is to study its various basic properties in connection with the Hurwitz metric.
