Geodesic
Isosystolic inequalities on two-dimensional Finsler tori
Florent Balacheff1 orcid ; Teo Gil Moreno de Mora2 orcid
1Universitat Autònoma de Barcelona, Bellaterra, Spain
2Université Paris-Est Créteil, Créteil, France; Universitat Autònoma de Barcelona, Bellaterra, Spain
EMS surveys in mathematical sciences, Tome 11 (2024) no. 2, pp. 205-233

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DOI

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.
DOI : 10.4171/emss/80
Classification : 53C23
Mots-clés : Busemann–Hausdorff and Holmes–Thompson area, isosystolic inequalities, Finsler metrics, stable norm, systole

Florent Balacheff  1   ; Teo Gil Moreno de Mora  2

1 Universitat Autònoma de Barcelona, Bellaterra, Spain
2 Université Paris-Est Créteil, Créteil, France; Universitat Autònoma de Barcelona, Bellaterra, Spain 
Florent Balacheff; Teo Gil Moreno de Mora. Isosystolic inequalities on two-dimensional Finsler tori. EMS surveys in mathematical sciences, Tome 11 (2024) no. 2, pp. 205-233. doi: 10.4171/emss/80
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     title = {Isosystolic inequalities on two-dimensional {Finsler} tori},
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     pages = {205--233},
     year = {2024},
     volume = {11},
     number = {2},
     doi = {10.4171/emss/80},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/80/}
}
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