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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.21596 |
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| _version_ | 1866908796699279360 |
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| author | Rott, Felix Xu, Zhe-Feng Zanardini, Matteo |
| author_facet | Rott, Felix Xu, Zhe-Feng Zanardini, Matteo |
| contents | We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curvature bound from above by zero. We investigate the link between the Ptolemy inequality and the hyperbolic inversion and establish some applications and rigidity properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21596 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lorentz meets Ptolemy Rott, Felix Xu, Zhe-Feng Zanardini, Matteo Differential Geometry Metric Geometry 53C23, 53C50, 53B30 We consider a Lorentzian analogue of the Ptolemy inequality and we prove that in the setting of globally hyperbolic spacetimes it is equivalent to a global timelike sectional curvature bound from above by zero. We investigate the link between the Ptolemy inequality and the hyperbolic inversion and establish some applications and rigidity properties. |
| title | Lorentz meets Ptolemy |
| topic | Differential Geometry Metric Geometry 53C23, 53C50, 53B30 |
| url | https://arxiv.org/abs/2601.21596 |