Isosystolic inequalities on two-dimensional Finsler tori
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 isosysto...
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:304142 |
| Online Access: | https://ddd.uab.cat/record/304142 https://dx.doi.org/urn:doi:10.4171/EMSS/80 |
| Access Level: | Open access |
| Keyword: | Busemann-Hausdorff and Holmes-Thompson area Finsler metrics Isosystolic inequalities Stable norm Systole |
| Summary: | 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. |
|---|