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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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https://hal.archives-ouvertes.fr/hal-03480483
Contributor : Vincent DESPRE Connect in order to contact the contributor
Submitted on : Tuesday, December 14, 2021 - 4:51:35 PM
Last modification on : Wednesday, March 30, 2022 - 9:38:55 AM
Long-term archiving on: : Tuesday, March 15, 2022 - 7:33:08 PM

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  • HAL Id : hal-03480483, version 1
  • ARXIV : 2011.03455

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Florent Balacheff, Vincent Despré, Hugo Parlier. Systoles and diameters of hyperbolic surfaces. Kyoto Journal of Mathematics, Duke University Press, 2022. ⟨hal-03480483⟩

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