A note on the affine plank conjecture

Abstract

In 1951, Bang posed the affine plank conjecture, which remains open: If a convex body in ${\mathbb{R}}^d$ is covered by planks, then the total relative width of the planks is at least one. We prove a lower bound of $2/(1+\sqrt{d})$ for this total relative width. The best previously known lower bound was $2/(1+d)$.