The triangular ratio metric is studied in a domain $G\subsetneq\mathbb{R}^n$, $n\geq2$. Several sharp bounds are proven for this metric, especially, in the case where the domain is the unit disk of the complex plane. The results are applied to study the Holder continuity of quasiconformal mappings.

中文翻译：

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单位圆盘中的三角比度量

在域 $G\subsetneq\mathbb{R}^n$, $n\geq2$ 中研究三角比率度量。这个度量有几个明确的界限，特别是在域是复平面的单位圆盘的情况下。结果用于研究拟共形映射的Holder连续性。