The symmetric plank problem, revisited

TL;DR

This paper provides a simplified proof of K. Ball's symmetric plank theorem, resolving the affine plank problem for symmetric convex bodies in Euclidean space.

Contribution

It offers a streamlined proof of a key geometric inequality, enhancing understanding of the symmetric plank problem.

Findings

Proof simplifies previous approaches

Confirms the validity of the symmetric plank theorem

Advances geometric inequalities in convex analysis

Abstract

We present a streamlined proof of K. Ball's symmetric plank theorem in $\mathbb{R}^d$, which solves the affine plank problem raised by Th. Bang for symmetric convex bodies.