Isosystolic inequalities on two-dimensional Finsler tori
Differential Geometry
2024-02-13 v3 Geometric Topology
Metric Geometry
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
@article{arxiv.2201.05010,
title = {Isosystolic inequalities on two-dimensional Finsler tori},
author = {Florent Balacheff and Teo Gil Moreno de Mora},
journal= {arXiv preprint arXiv:2201.05010},
year = {2024}
}
Comments
Accepted version to be published in the EMS Surv. Math. Sci