多夫戈舍伊-哈里里-武里宁度量和格罗莫夫双曲性

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-06-20 DOI:10.1007/s00013-024-02021-w

Qingshan Zhou, Zhoucheng Zheng, Saminathan Ponnusamy, Tiantian Guan

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引用次数: 0

摘要

2016 年，Dovgoshey 等人引入了欧几里得空间 \(\mathbb {R}^k\) 的适当子域 G 上的度量 \(\zeta \)，并研究了它与几种双曲型度量的联系。在本文中，我们考虑了\((G,\zeta )\)的格罗莫夫双曲性，并证明了在 G 的欧几里得边界和配有视觉度量的\((G,\zeta )\)的格罗莫夫边界之间存在一个自然的类对称同构。

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Dovgoshey–Hariri–Vuorinen’s metric and Gromov hyperbolicity

In 2016, Dovgoshey et al. introduced a metric \(\zeta \) on proper subdomains G of Euclidean spaces \(\mathbb {R}^k\) and studied its connection with several hyperbolic type metrics. In this paper, we consider the Gromov hyperbolicity of \((G,\zeta )\) and show that there is a natural quasisymmetric homeomorphism between the Euclidean boundary of G and the Gromov boundary of \((G,\zeta )\) equipped with a visual metric.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.