与域边界相关的新度量

Pub Date : 2024-05-23 DOI:10.1007/s40315-024-00545-4

Xingchen Song, Gendi Wang

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引用次数: 0

摘要

在本文中，我们引入了一种与托勒密空间（X, d）的域边界相关的新度量（\(\tilde{c}\)）。此外，我们还研究了单位球莫比乌斯变换下的\(\tilde{c}\)度量球和一些相关的双曲型度量球在\({\mathbb {R}}^n.\) 子域中的包容关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A New Metric Associated with the Domain Boundary

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A New Metric Associated with the Domain Boundary

In this paper, we introduce a new metric \(\tilde{c}\) which is associated with the domain boundary for a Ptolemy space (X, d). Moreover, we study inclusion relations of \(\tilde{c}\) metric balls and some related hyperbolic type metric balls in subdomains of \({\mathbb {R}}^n.\) In addition, we study distortion properties of the \(\tilde{c}\) metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the \(\tilde{c}\) metric.

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