Systoles and diameters of hyperbolic surfaces
Geometric Topology
2023-04-03 v2 Differential Geometry
Abstract
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent) upper bound.
Cite
@article{arxiv.2011.03455,
title = {Systoles and diameters of hyperbolic surfaces},
author = {Florent Balacheff and Vincent Despré and Hugo Parlier},
journal= {arXiv preprint arXiv:2011.03455},
year = {2023}
}
Comments
13 pages, 9 figures