Isosystolic inequalities on two-dimensional Finsler tori

2022/01/13 by Florent Balacheff, Balacheff, Florent, Teo Gil Moreno de Mora +1
Physics and Astronomy · #53C23 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2201.05010

openalex publication_date 2022/01/13 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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 π/4.

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