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arXiv · 2405.07818

New lower bound on ball packing density in high-dimensional hyperbolic spaces

Irene Gil Fernández·Jaehoon Kim·Hong Liu·Oleg Pikhurko
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Abstract

We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor Ω(m(R+\ln m)) as m tends to infinity. This is done by applying the recent theorem of Campos, Jenssen, Michelen and Sahasrabudhe on independent sets in graphs with sparse neighbourhoods.

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Irene Gil Fernández, Jaehoon Kim, Hong Liu, Oleg Pikhurko. 2024-09-26. New lower bound on ball packing density in high-dimensional hyperbolic spaces. https://arxiv.org/abs/2405.07818

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