Answering a question about triangle inequality suggested by R. Li, Barrlund [The p-relative distance is a metric. SIAM J Matrix Anal Appl. 1999;21:699.702] introduced a distance function which is a metric on a subdomain of ${\mathbb{R}}^n.$ We study this Barrlund metric and give sharp bounds for it in terms of other metrics of current interest. We also prove sharp distortion results for the Barrlund metric under quasiconformal maps.

中文翻译：

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Barrlund 距离函数和拟共形映射

回答 R. Li, Barrlund 提出的关于三角不等式的问题 [p 相对距离是一个度量。SIAM J Matrix Anal Appl。1999;21:699.702] 介绍了一个距离函数，它是一个子域的度量${\mathbb{电阻}}^n.$我们研究了这个 Barrlund 指标，并根据当前感兴趣的其他指标给出了明确的界限。我们还证明了准共形映射下 Barrlund 度量的尖锐失真结果。