Systoles and diameters of hyperbolic surfaces

Florent Balacheff; Vincent Despré; Hugo Parlier

doi:10.1215/21562261-2022-0040

Systoles and diameters of hyperbolic surfaces

Florent Balacheff, Vincent Despré, Hugo Parlier

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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.

Original language	English
Pages (from-to)	211 - 222
Number of pages	12
Journal	Kyoto Journal of Mathematics
Volume	63
Issue number	1
DOIs	https://doi.org/10.1215/21562261-2022-0040
Publication status	Published - 1 Feb 2023

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Systoles and diameters of hyperbolic surfaces

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