Isosystolic inequalities on two-dimensional Finsler tori
Florent Balacheff
Universitat Autònoma de Barcelona, Bellaterra, SpainTeo Gil Moreno de Mora
Université Paris-Est Créteil, Créteil, France; Universitat Autònoma de Barcelona, Bellaterra, Spain
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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 -torus with unit systole is at least equal to .
Cite this article
Florent Balacheff, Teo Gil Moreno de Mora, Isosystolic inequalities on two-dimensional Finsler tori. EMS Surv. Math. Sci. (2024), published online first
DOI 10.4171/EMSS/80