[en] 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.
Disciplines :
Mathematics
Author, co-author :
Balacheff, Florent ✱; Department of Mathematics, Universitat Autònoma de Barcelona, Spain
Despré, Vincent ✱; Polytech Nancy, Université de Lorraine, Loria, France
PARLIER, Hugo ✱; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
✱ These authors have contributed equally to this work.
External co-authors :
yes
Language :
English
Title :
Systoles and diameters of hyperbolic surfaces
Publication date :
2023
Journal title :
Journal of Mathematics of Kyoto University
ISSN :
0023-608X
Publisher :
Duke University Press
Volume :
63
Issue :
1
Pages :
211 - 222
Peer reviewed :
Peer reviewed
Funding text :
Balacheff was supported by the FSE/AEI/MICINN grant RYC-2016-19334 “Local and Global Systolic Geometry and Topology,” the AGAUR grant 2017-SGR-1725, and the FEDER/AEI/MICIU grant PGC2018-095998-B-I00 “Local and Global Invariants in Geometry.” Despréand Parlier were supported by the ANR/FNR project SoS, INTER/ANR/16/11554412/SoS, ANR-17-CE40-0033.
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