C~度量与三角比度量的精确比较及其应用
Sharp Comparison between the C~ Metric and the Triangular Ratio Metric and Its Applications
摘要: 本文研究了一个与边界相关的双曲型度量 和三角比度量的精确比较关系。应用该关系，得到了C~度量与Cassini度量、双曲度量和距离比度量之间的比较不等式。特别地，证明了这些不等式的精确性。此外，还通过C~度量与三角比度量之间的比较关系得到了在C~度量下bi-Lipschitz映射的拟共形性。
Abstract: This article investigates the sharp comparison between a boundary-related hyperbolic type metric C~ and the triangular ratio metric. By applying this relationship, comparisons between the C~ metric and the Cassinian metric, the hyperbolic metric, and the distance ratio metric are obtained. In particular, we show the accuracy of these inequalities. Additionally, the quasi-conformality of the bi-Lipschitz mapping under the C~ metric is also obtained by comparing it with the triangular ratio metric.
文章引用：宋星晨, 王根娣. C~度量与三角比度量的精确比较及其应用[J]. 理论数学, 2023, 13(12): 3653-3662. https://doi.org/10.12677/PM.2023.1312379

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