Estimates for the extremal sections of \(\ell ^n_p\)-balls
type: Item
instance of: scholarly article
title: Estimates for the extremal sections of \(\ell ^n_p\)-balls
zbMATH Open document ID: 1217.52005
author: Dan Ma
author: Binwu He
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-02-09T00:00:00Z
review text: Let \(p\in [1, +\infty]\), \(B_p^n\) denote the unit ball of \(\ell_p^n\), \(r_{n,p}= (\text{vol}_n(B_p^n))^{-1/n}\), so \(r_{n,p}B_p^n\) is the normalized volume \(\ell ^n_p\)-ball. The main result of the paper is the upper estimate by \(\sqrt{\pi e}\) of the \((n-1)\)-dimensional volume of every central hyperplane section of the normalized \(\ell ^n_p\)-ball. In the proof the authors show by direct calculation that the isotropic constant of \(B_p^n\) takes its smallest value when \(p=2\) and then apply the well-known estimates of the hyperplane sections through the corresponding isotropic constant.
reviewed by: Vladimir Kadets
Mathematics Subject Classification ID: 52A23
Mathematics Subject Classification ID: 52A21
Mathematics Subject Classification ID: 46B06
zbMATH DE Number: 5848915
zbMATH Keywords: \(\ell ^n_p\)-space
zbMATH Keywords: slicing problem
zbMATH Keywords: isotropic constant
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.11.058
OpenAlex ID: W2031669028
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DOI: 10.1016/J.JMAA.2010.11.058
description: scientific article; zbMATH DE number 5848915