Mean width inequalities for isotropic measures
type: Item
instance of: scholarly article
title: Mean width inequalities for isotropic measures
zbMATH Open document ID: 1250.52003
author: Ai-Jun Li
author: Gangsong Leng
published in: Mathematische Zeitschrift
publication date: 2012-05-08T00:00:00Z
review text: The authors establish Barthe's mean width inequalities for continuous isotropic measures by a direct approach rather than using the Brascamp-Lieb inequality. The following results are obtained: among the convex hulls of the support of isotropic measures on \(S^{n-1}\), the regular simplex inscribed in the Euclidean unit ball has maximal \(\ell\)-norm; in the dual situation, there is a reverse result for their polar bodies. Moreover, the case of even isotropic measures is also investigated.
reviewed by: Anatoliy Milka
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 6031793
zbMATH Keywords: mean width inequality
zbMATH Keywords: isotropic measure
zbMATH Keywords: \(\ell \)-norm
zbMATH Keywords: Ball-Barthe inequality
MaRDI profile type: Publication
full work available at URL: s00209-011-0843-5
OpenAlex ID: W2009450586
cites work: Q4387224
cites work: Convex geometry and functional analysis
cites work: Q3828510
cites work: Shadows of Convex Bodies
cites work: Inégalités de Brascamp-Lieb et convexité
cites work: An extremal property of the mean width of the simplex
cites work: On a reverse form of the Brascamp-Lieb inequality
cites work: Q4664558
cites work: John's decomposition of the identity in the non-convex case
cites work: From John to Gauss--John positions via dual mixed volumes
cites work: Extremal problems and isotropic positions of convex bodies
cites work: Q2702143
cites work: John's theorem for an arbitrary pair of convex bodies
cites work: John's decomposition in the general case and applications
cites work: Application of an idea of Voronoĭ to John type problems
cites work: An arithmetic proof of John's ellipsoid theorem
cites work: Ellipsoids defined by Banach ideal norms
cites work: Ellipsoids and matrix-valued valuations
cites work: A new ellipsoid associated with convex bodies
cites work: Volume inequalities for subspaces of \(L_p\)
cites work: $L_p$ John Ellipsoids
cites work: Volume inequalities for isotropic measures
cites work: A volume inequality for polar bodies
cites work: Q4040885
cites work: Q4839535
cites work: Q4249215
cites work: Q5287551
cites work: Q4041061
DOI: 10.1007/S00209-011-0843-5
description: scientific article; zbMATH DE number 6031793