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arXiv · 2201.05010

Isosystolic inequalities on two-dimensional Finsler tori

Florent Balacheff·Teo Gil Moreno de Mora
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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 $2$-torus with unit systole is at least equal to $\pi/4$.

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Florent Balacheff, Teo Gil Moreno de Mora. 2022-01-13. Isosystolic inequalities on two-dimensional Finsler tori. https://arxiv.org/abs/2201.05010

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