A remark on the slicing problem

Abstract

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I1(K,Zq{ring operator}(K))=∫K{norm of matrix}〈{dot operator},x〉{norm of matrix}Lq(K)dx. We show that an upper bound of the form I1(K,Zq{ring operator}(K))≤C1qsnLK2, with 1/2. ≤. s≤. 1, leads to the estimate. Ln≤C2n4lognq1-s2, where Ln:=max{LK:K is an isotropic convex body in Rn}. © 2011.