Inequalities on Six Points in a $\mathrm{CAT}(0)$ Space
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909538186166272 |
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| author | Toyoda, Tetsu |
| author_facet | Toyoda, Tetsu |
| contents | We establish a family of inequalities that hold true on any $6$ points in any $\mathrm{CAT}(0)$ space. We prove that the validity of these inequalities does not follow from any properties of $5$-point subsets of $\mathrm{CAT}(0)$ spaces. In particular, the validity of these inequalities does not follow from the $\mathrm{CAT}(0)$ $4$-point condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities on Six Points in a $\mathrm{CAT}(0)$ Space Toyoda, Tetsu Metric Geometry 30L15, 53C23, 51F99 We establish a family of inequalities that hold true on any $6$ points in any $\mathrm{CAT}(0)$ space. We prove that the validity of these inequalities does not follow from any properties of $5$-point subsets of $\mathrm{CAT}(0)$ spaces. In particular, the validity of these inequalities does not follow from the $\mathrm{CAT}(0)$ $4$-point condition. |
| title | Inequalities on Six Points in a $\mathrm{CAT}(0)$ Space |
| topic | Metric Geometry 30L15, 53C23, 51F99 |
| url | https://arxiv.org/abs/2411.13877 |