Inequalities and bilipschitz conditions for triangular ratio metric
Inequalities and bilipschitz conditions for triangular ratio metric
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DOI：
10.1216/rmj-2017-47-4-1121
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发表时间：
2014-11
影响因子：
0.8
通讯作者：
Parisa Hariri;M. Vuorinen;Xiaohui Zhang
中科院分区：
文献类型：
--
作者：
Parisa Hariri;M. Vuorinen;Xiaohui Zhang
设$G \subsetneq \mathbb{R}^n$是一个域，$d_1$和$d_2$是$G$上的两个度量。我们比较的几何定义的两个度量彼此的几对度量。我们研究的度量包括距离比度量、三角比度量和视角度量。最后，我们应用我们的结果来研究与这些指标相关的Lipschitz映射。
Let $G \subsetneq \mathbb{R}^n$ be a domain and let $d_1$ and $d_2$ be two metrics on $G$. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio metric, the triangular ratio metric and the visual angle metric. Finally we apply our results to study Lipschitz maps with respect to these metrics.