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Journal Articles Kyoto Journal of Mathematics Year : 2022

Systoles and diameters of hyperbolic surfaces


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



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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