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

Abstract

We prove that given a finite collection of cylinders in ${\mathbb{R}}^3$ 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.

6 pages

Cited by in corpus (1)

• Piercing intersecting convex sets