Systoles and diameters of hyperbolic surfaces

Florent Balacheff (1) , Vincent Despré (2) , Hugo Parlier (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
3 University of Luxembourg [Luxembourg]

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".

Mots clés: 2020 Mathematics Subject Classification: Primary: 32G15; 53C22; 57K20. Secondary: 30F60 systole; systolic inequalities; diameter; geodesics; hyperbolic surfaces

Domaines: Topologie géométrique [math.GT]

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