Systoles and diameters of hyperbolic surfaces
arXiv:2011.03455 · doi:10.1215/21562261-2022-0040
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.
13 pages, 9 figures