A remark on the slicing problem Academic Article uri icon

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.

author list (cited authors)

  • Giannopoulos, A., Paouris, G., & Vritsiou, B.

citation count

  • 2

publication date

  • February 2012