@inbook{04d92753ca0345619a8b230c5a8e75b0,

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 = "10.1007/978-3-030-46762-3_2",

language = "אנגלית",

series = "Lecture Notes in Mathematics",

publisher = "Springer",

pages = "43--63",

booktitle = "Lecture Notes in Mathematics",

}