Bounds on hyperbolic sphere packings: On a conjecture by Cohn and Zhao
Metric Geometry
2026-03-23 v2 Group Theory
Probability
Abstract
We prove sphere packing density bounds in hyperbolic space (and more generally irreducible symmetric spaces of noncompact type), which were conjectured by Cohn and Zhao and generalize Euclidean bounds by Cohn and Elkies. We work within the Bowen-Radin framework of packing density and replace the use of the Poisson summation formula in the proof of the Euclidean bound by Cohn and Elkies with an analogous formula arising from methods used in the theory of mathematical quasicrystals.
Keywords
Cite
@article{arxiv.2411.07139,
title = {Bounds on hyperbolic sphere packings: On a conjecture by Cohn and Zhao},
author = {Maximilian Wackenhuth},
journal= {arXiv preprint arXiv:2411.07139},
year = {2026}
}
Comments
6 pages, minor changes, accepted for publication at C. R. Math. Acad. Sci. Paris