On the regularity radius of Delone sets in R3

Authors

Nikolay Dolbilin
Alexey Garber, The University of Texas Rio Grande Valley
Undine Leopold
Egon Schulte

Document Type

Article

Publication Date

2019

Abstract

We complete the proof of the upper bound ρ^3≤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.

Recommended Citation

Dolbilin, Nikolay, Alexey Garber, Undine Leopold, and Egon Schulte. 2019. “On the Regularity Radius of Delone Sets in $\mathbb{R}^3$.” ArXiv:1909.05805 [Math], September. http://arxiv.org/abs/1909.05805.