Span度量及其高阶曲率的边界性态
Boundary behaviour of the Span metric and its higher-order curvatures
摘要：
本文利用标度原理研究了非连通Jordan平面域上跨距度量及其高阶曲率的边界性质。并给出了该度量在连通Jordan域的边界点附近的局部化.此外，我们得到边界尖锐估计这个度量$ C^2 $ -光滑有界域，因此，这个度量是可比的Carathéodory和小林度量在这些领域。
英文摘要：
In this note, we use scaling principle to study the boundary behaviour of the span metric and its higher-order curvatures on finitely connected Jordan planar domains. A localization of this metric near boundary points of finitely connected Jordan domains is also obtained. Further, we obtain boundary sharp estimates for this metric on $ C^2 $-smooth bounded domains and consequently, this metric is comparable to the Carathéodory and the Kobayashi metrics on these domains.
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