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Journal Articles Kyoto Journal of Mathematics Year : 2022

Systoles and diameters of hyperbolic surfaces

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. asymptotic question was recently settled by Budzinski, Curien and Petri [6] where they * Supported by the FSE/AEI/MICINN grant RYC-2016-19334 "Local and global systolic geometry and topology" and the FEDER/AEI/MICIU grant PGC2018-095998-B-I00 "Local and global invariants in geometry".
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Dates and versions

hal-03480483 , version 1 (14-12-2021)

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Florent Balacheff, Vincent Despré, Hugo Parlier. Systoles and diameters of hyperbolic surfaces. Kyoto Journal of Mathematics, 2022, ⟨10.1215/21562261-2022-0040⟩. ⟨hal-03480483⟩
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