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

Bo’az Klartag; Galyna V. Livshyts

doi:https://doi.org/10.1007/978-3-030-46762-3_2

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

Bo’az Klartag, Galyna V. Livshyts

Tel Aviv University, Weizmann Institute of Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-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 language	English
Title of host publication	Lecture Notes in Mathematics
Editors	B Klartag, E Milman
Pages	43-63
Number of pages	21
DOIs	https://doi.org/10.1007/978-3-030-46762-3_2
State	Published - 2020

Publication series

Name	Lecture Notes in Mathematics
Volume	2266

Keywords

Convex bodies
Log-concave

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Access to Document

https://doi.org/10.1007/978-3-030-46762-3_2

https://arxiv.org/abs/1810.06189License: Other

Cite this

@inbook{7543fa2974a04dba9a96b2ec65e3e790,

title = "The Lower Bound for Koldobsky{\textquoteright}s Slicing Inequality via Random Rounding",

abstract = "We study the lower bound for Koldobsky{\textquoteright}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.",

keywords = "Convex bodies, Log-concave",

author = "Bo{\textquoteright}az Klartag and Livshyts, {Galyna V.}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

doi = "https://doi.org/10.1007/978-3-030-46762-3_2",

language = "الإنجليزيّة",

isbn = "978-3-030-46761-6",

series = "Lecture Notes in Mathematics",

pages = "43--63",

editor = "B Klartag and E Milman",

booktitle = "Lecture Notes in Mathematics",

}

TY - CHAP

T1 - The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding

AU - Klartag, Bo’az

AU - Livshyts, Galyna V.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Convex bodies

KW - Log-concave

UR - http://www.scopus.com/inward/record.url?scp=85088503503&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/978-3-030-46762-3_2

DO - https://doi.org/10.1007/978-3-030-46762-3_2

M3 - فصل

SN - 978-3-030-46761-6

T3 - Lecture Notes in Mathematics

SP - 43

EP - 63

BT - Lecture Notes in Mathematics

A2 - Klartag, B

A2 - Milman, E

ER -

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

Abstract

Publication series

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this