The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding

Bo’az Klartag*, Galyna V. Livshyts

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We study the lower bound for Koldobsky’s slicing inequality. We show that there exists a measure μ and a symmetric convex body Kn, such that for all (Formula Presented) and all t,μ+(K∩(ξ⊥+tξ))≤cnμ(K)|K|−1n. Our bound is optimal, up to the value of the universal constant. It improves slightly upon the results of the first named author and Koldobsky, which included a doubly-logarithmic error. The proof is based on an efficient way of discretizing the unit sphere.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
Number of pages21
StatePublished - 2020

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692


  • Convex bodies
  • Log-concave


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