尼科洛夫-安德烈耶夫公设与格罗莫夫双曲性

IF 1.1 3区数学 Q1 MATHEMATICS Mediterranean Journal of Mathematics Pub Date : 2024-04-29 DOI:10.1007/s00009-024-02655-8

Qianghua Luo, Antti Rasila, Ye Wang, Qingshan Zhou

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引用次数: 0

摘要

在本文中，我们证明了尼科洛夫和安德烈耶夫最近引入的配备度量 \(i_\{Omega }\) 的 \(\mathbb {R}^n\) 的适当子域 \(\Omega \) 是格罗莫夫双曲的。我们还证明了 \(\Omega \) 的欧几里得边界（关于 \(\overline\mathbb {R}^n}\) ）和 \((\Omega ,i_\Omega )\) 的格罗莫夫边界之间存在自然的类对称对应关系。

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The Nikolov–Andreev Metric and Gromov Hyperbolicity

In this paper, we prove that a proper subdomain \(\Omega \) of \(\mathbb {R}^n\) equipped with the metric \(i_{\Omega }\), recently introduced by Nikolov and Andreev, is Gromov hyperbolic. We also show that there is a natural quasisymmetric correspondence between the Euclidean boundary of \(\Omega \) (with respect to \(\overline{\mathbb {R}^n}\)) and the Gromov boundary of \((\Omega ,i_\Omega )\).

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来源期刊

Mediterranean Journal of Mathematics 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

261

审稿时长

6-12 weeks

期刊介绍： The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003. The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience. In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.