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arXiv · 1909.05805

On the regularity radius of Delone sets in $\mathbb{R}^3$

Nikolay Dolbilin·Alexey Garber·Undine Leopold·Egon Schulte
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Abstract

We complete the proof of the upper bound $\hatρ_3\leq 10R$ for the regularity radius of Delone sets in three-dimensional Euclidean space. Namely, summing up the results obtained earlier, and adding the missing cases, we show that if all $10R$-clusters of a Delone set $X$ with parameters $(r,R)$ are equivalent, then $X$ is a regular system.

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Nikolay Dolbilin, Alexey Garber, Undine Leopold, Egon Schulte. 2019-09-12. On the regularity radius of Delone sets in $\mathbb{R}^3$. https://doi.org/10.1007/s00454-021-00292-6

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