A remark on the slicing problem

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I1(K,Z◦q(K)) = K ·, x Lq(K) dx. We show that an upper bound of the form I1(K,Z◦q(K)) C1qs√nL2 K, with 1/2 s 1, leads to the estimate Ln C2 √4 n log n q 1−s 2 , where Ln := max{LK: K is an isotropic convex body in Rn}. © 2011 Published by Elsevier Inc.