Kissing numbers of closed hyperbolic manifolds
Geometric Topology
2019-05-28 v1 Differential Geometry
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.
Cite
@article{arxiv.1905.11083,
title = {Kissing numbers of closed hyperbolic manifolds},
author = {Maxime Fortier Bourque and Bram Petri},
journal= {arXiv preprint arXiv:1905.11083},
year = {2019}
}
Comments
16 pages