On the densest packing of polycylinders in any dimension

Abstract

Using transversality and a dimension reduction argument, a result of A. Bezdek and W. Kuperberg is applied to polycylinders ${\mathbb{D}}^2\times {\mathbb{R}}^n$, showing that the optimal packing density is $\pi /\sqrt{12}$ in any dimension.

arXiv commentEdited to reflect acknowledgements in the published version

References in corpus (1)

• Upper bounds on packing density for circular cylinders with high aspect ratio