A Note about Bezdek's Conjecture on Covering an Annulus by Strips

Abstract

A closed plane region between two parallel lines is called a strip. András Bezdek posed the following conjecture: For each convex region $K$ there is an $\varepsilon>0$ such that if $\varepsilon K$ lies in the interior of $K$ and the annulus $K\backslash \varepsilon K$ is covered by finitely many strips, then the sum of the widths of the strips must be at least the minimal width of $K$. In this paper, we consider problems which are related to the conjecture.