Isosystolic inequalities on two-dimensional Finsler tori

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 isosysto...

Full description

Bibliographic Details
Authors: Balacheff, Florent Nicolas|||0000-0001-9770-2954, Gil Moreno de Mora Sardà, Teo|||0009-0003-9464-1107
Format: article
Publication Date:2024
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:304142
Online Access:https://ddd.uab.cat/record/304142
https://dx.doi.org/urn:doi:10.4171/EMSS/80
Access Level:Open access
Keyword:Busemann-Hausdorff and Holmes-Thompson area
Finsler metrics
Isosystolic inequalities
Stable norm
Systole
Description
Summary: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.