The Nikolov–Andreev Metric and Quasimöbius Maps in Banach Spaces

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发表日期：

2025年10月5日

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Qingshan Zhou,
Zhoucheng Zheng,
Peiying Huo

摘要

This paper focuses on large-scale geometric properties of the Nikolov–Andreev metric in proper subdomains of real Banach spaces in the sense of Gromov. First, we demonstrate that every proper subdomain equipped with the Nikolov–Andreev metric is Gromov $\delta _0$ $δ_{0}$ -hyperbolic with $\delta _0=\log 4$ $δ_{0} = log 4$ . Next, we prove that there is a natural quasimöbius correspondence between the norm boundary and the Gromov boundary endowed with a visual metric. Finally, we establish the quasi-invariance of the Nikolov–Andreev metric under quasimöbius maps between proper domains of real Banach spaces.