The purpose of this note is to use the scaling principle to study the boundary behaviour of some conformal invariants on planar domains. The focus is on the Aumann–Carathéodory rigidity constant, the higher order curvatures of the Carathéodory metric and a conformal metric arising from holomorphic quadratic differentials.

中文翻译：

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平面域上一些保形不变量的边界行为

本文的目的是使用缩放原理来研究平面域上某些共形不变量的边界行为。重点是Aumann–Carathéodory刚度常数，Carathéodory度量的高阶曲率以及由全纯二次微分产生的共形度量。