Isosystolic inequalities on two-dimensional Finsler tori
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911774337400832 |
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| author | Balacheff, Florent de Mora, Teo Gil Moreno |
| author_facet | Balacheff, Florent de Mora, Teo Gil Moreno |
| contents | In this article we survey all known optimal isosystolic inequalities on two-dimensional Finsler tori involving the following two central notions of Finsler area: the Busemann-Hausdorff area and the Holmes-Thompson area. We also complete the panorama by establishing the following new optimal isosystolic inequality that is deduced from prior work by Burago and Ivanov: the Busemann-Hausdorff area of a Finsler reversible $2$-torus with unit systole is at least equal to $π/4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_05010 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Isosystolic inequalities on two-dimensional Finsler tori Balacheff, Florent de Mora, Teo Gil Moreno Differential Geometry Geometric Topology Metric Geometry 53C23 In this article we survey all known optimal isosystolic inequalities on two-dimensional Finsler tori involving the following two central notions of Finsler area: the Busemann-Hausdorff area and the Holmes-Thompson area. We also complete the panorama by establishing the following new optimal isosystolic inequality that is deduced from prior work by Burago and Ivanov: the Busemann-Hausdorff area of a Finsler reversible $2$-torus with unit systole is at least equal to $π/4$. |
| title | Isosystolic inequalities on two-dimensional Finsler tori |
| topic | Differential Geometry Geometric Topology Metric Geometry 53C23 |
| url | https://arxiv.org/abs/2201.05010 |