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

Bo’az Klartag, Galyna V. Livshyts

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

Abstract

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
PublisherSpringer
Pages43-63
Number of pages21
DOIs
StatePublished - 2020

Publication series

NameLecture Notes in Mathematics
Volume2266
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692

Keywords

  • Convex bodies
  • Log-concave

Fingerprint

Dive into the research topics of 'The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding'. Together they form a unique fingerprint.

Cite this