Kissing numbers of closed hyperbolic manifolds

Maxime Fortier Bourque; Bram Petri

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arXiv · 1905.11083

Kissing numbers of closed hyperbolic manifolds

Maxime Fortier Bourque·Bram Petri

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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.

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BibTeX RIS

Maxime Fortier Bourque, Bram Petri. 2019-05-27. Kissing numbers of closed hyperbolic manifolds. https://arxiv.org/abs/1905.11083

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