On Ball's conjectured Santaló type inequality

Károly J. Böröczky, Konstantinos Patsalos, Christos Saroglou

We prove that if $K$ is a symmetric and isotropic convex body in ${\mathbb{R}}^n$, then $$\int_K\langle x,u\rangle^2\,dx\int_{K^\circ}\langle x,u\rangle^2\,dx\leq \left(\int_{B_2^n}\…