2 problems

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The strong regularity-radius conjecture for Delone sets
Let $X$ be a Delone set in $\mathbb{R}^d$ with parameters $(r,R)$ , where $R$ is the radius of a largest empty ball, and let $\hat{\rho}_d=\hat{\rho}_d(r,R)$ be the smallest radius…
Conjectureopendelone-sets discrete-geometry regularity-radiusarXiv posted 2 days ago
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Rump's conjecture on the regularity-radius bound
Rump's conjecture. The factor in the upper bound can be chosen as
Conjectureopeninterval-analysis regularity-radiusarXiv posted 2 days ago

The strong regularity-radius conjecture for Delone sets