4 problems

Let a non-parallel cylinder packing be a packing of congruent infinite circular cylinders in $\mathbb{R}^3$ such that no two cylinder axes are parallel. For a packing $\mathcal C$,…

Let $\mathcal C=\{C_i\}_{i=1}^{\infty}$ be a non-parallel cylinder packing in $\mathbb{R}^3$, and let $(\delta^{*})^{-}(\mathcal C)$ denote its translation-invariant lower density.…

Consider four parallel non-intersecting cylinders of radius $r=1+\sqrt{2}$ touching the unit ball, in the configuration regime studied in the paper. Four-cylinder position conjectu…

Consider configurations of four cylinders in the setting above, represented by points on the configuration manifold and the distinguished curve obtained from the three relevant mut…