A remark on the slicing problem

2011/07/22 by Apostolos Giannopoulos, Giannopoulos, Apostolos, Grigoris Paouris +3
Computer Science · Mathematics · #46B06 #52A23 #52A40 #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.FA #math.MG #msc:46B06 #msc:52A23 #msc:52A40

paper · pdf · doi:10.48550/arxiv.1107.4527

24 pages

arxiv created 2011/07/22 · openalex publication_date 2011/07/22 · arxiv updated 2011/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to describe a reduction of the slicing problem to the study of the parameter I₁(K,Z_q^o(K))=∫_K ||< :, x> ||_Lq(K)dx. We show that an upper bound of the form I₁(K,Z_q^o(K))≤ C₁q^s√(n)L_K², with 1/2≤ s≤ 1, leads to the estimate L_n≤ \fracC₂√[4]nlog(n) q^(1-s)/2, where L_n:= max L_K : K is an isotropic convex body in Rⁿ.

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