Pairwise intersecting convex sets and cylinders in $\R^3$

Imre Barany

Published 2021-04-05Version 1

We prove that given a finite collection of cylinders in $\R^3$ with the property that any two them intersect, then there is a line intersecting an $\alpha$ fraction of the cylinders where $\alpha=\frac 1{28}$. This is a special case of an interesting conjecture.