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Isosystolic inequalities on two-dimensional Finsler tori

Differential Geometry 2024-02-13 v3 Geometric Topology Metric Geometry

Abstract

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 22-torus with unit systole is at least equal to π/4\pi/4.

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Cite

@article{arxiv.2201.05010,
  title  = {Isosystolic inequalities on two-dimensional Finsler tori},
  author = {Florent Balacheff and Teo Gil Moreno de Mora},
  journal= {arXiv preprint arXiv:2201.05010},
  year   = {2024}
}

Comments

Accepted version to be published in the EMS Surv. Math. Sci