descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Aug 2022Embargo end date: 01 Jan 2019 English Publisher:Project MUSEJournal:American Journal of Mathematics, volume 144, pages 1,067-1,085 (eissn: 1080-6377,

Authors: Fortier-Bourque, Maxime; Petri, Bram;

doi: 10.1353/ajm.2022.0023 , 10.48550/arxiv.1905.11083

arXiv: http://arxiv.org/abs/1905.11083

Kissing numbers of closed hyperbolic manifolds

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Abstract

We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of Parlier for surfaces. We also obtain bounds on the number of primitive closed geodesics with length in a given interval that are uniform for all closed hyperbolic manifolds with bounded geometry. The proofs rely on the Selberg trace formula.

16 pages

Keywords

Mathematics - Differential Geometry, Mathematics - Geometric Topology, Differential Geometry (math.DG), FOS: Mathematics, Geometric Topology (math.GT)

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