Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929597262594048 |
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| author | You, Qizheng Zhang, Jiawen |
| author_facet | You, Qizheng Zhang, Jiawen |
| contents | In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying the 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 in [2]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07991 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity You, Qizheng Zhang, Jiawen Metric Geometry In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying the 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 in [2]. |
| title | Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2307.07991 |