{"title":"Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity","authors":"Qizheng You, Jiawen Zhang","doi":"10.1017/s0017089524000065","DOIUrl":null,"url":null,"abstract":"<p>In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying Gromov’s <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308121158651-0633:S0017089524000065:S0017089524000065_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$4$</span></span></img></span></span>-point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.</p>","PeriodicalId":50417,"journal":{"name":"Glasgow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Glasgow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0017089524000065","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying Gromov’s $4$-point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.
期刊介绍：
Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics.
The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.
$4$-point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.
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