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, showing that the optimal packing density of $\mathbb{D}^2\times \mathbb{R}^n$ equals $\pi/\sqrt{12}$ for all $n \ge 0$.

Comments and Corrigenda:

This paper was split before publication. In the published version, the second sentence “The closed unit interval is denoted by $\mathbb{I}$.” is extraneous.