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arXiv · 2310.06943

On non-parallel cylinder packings

Ofek Eliyahu
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Abstract

In this paper we will discuss optimal lower and upper density of non-parallel cylinder packings in $R^{3}$ and similar problems. The main result of the paper is a proof of the conjecture of K. Kuperberg for upper density (existence of a non-parallel cylinder packing with upper density ${\pi}/{\sqrt{12}}$). Moreover, we prove that for every $\varepsilon > 0$ there exists a nonparallel cylinder packing with lower density greater then ${\pi}/{6} - \varepsilon$.

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Ofek Eliyahu. 2023-10-10. On non-parallel cylinder packings. https://arxiv.org/abs/2310.06943

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