Strong slicing conjecture (general case) for convex bodies

Prove that for every convex body K ⊂ ℝ^n, the isotropic constant satisfies L_K ≤ L_{A_n}, where A_n denotes the n-dimensional regular simplex with barycenter at the origin.

Background

The strong slicing conjecture in the general (non-symmetric) setting asserts that the regular simplex maximizes the isotropic constant among all convex bodies in fixed dimension n. The authors list it explicitly as Conjecture 2.

This conjecture connects to Mahler’s conjecture via results of Klartag and others: establishing the strong slicing conjecture implies Mahler’s conjecture in the same dimension.