Fortier-Bourque, M. and Petri, B. (2019) Kissing numbers of closed hyperbolic manifolds. arXiv, (Unpublished)
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189099.pdf - Submitted Version 358kB |
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.
| Item Type: | Articles |
|---|---|
| Status: | Unpublished |
| Refereed: | No |
| Glasgow Author(s) Enlighten ID: | Fortier-Bourque, Dr Maxime |
| Authors: | Fortier-Bourque, M., and Petri, B. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | arXiv |
| Copyright Holders: | Copyright © 2019 The Authors |
| Publisher Policy: | Reproduced with the permission of the authors |
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