Some \(\log\)-Minkowski inequalities for \(L_p\)-mixed affine surface area
type: Item
instance of: scholarly article
title: Some \(\log\)-Minkowski inequalities for \(L_p\)-mixed affine surface area
zbMATH Open document ID: 1475.52005
author: Yanyan Li
published in: Positivity
publication date: 2021-08-16T00:00:00Z
review text: The \(L_p\) Brunn-Minkowski theory is an important theory in convex geometry which has received widespread attention; the related results are very rich when \(p\geq1\). Since the outstanding works of Böröczky, Lutwak, Yang and Zhang [\textit{K. Böröczky jun.} et al., Adv. Math. 231, No. 3--4, 1974--1997 (2012; Zbl 1258.52005); J. Am. Math. Soc. 26, No. 3, 831--852 (2013; Zbl 1272.52012)], the \(L_p\) Brunn-Minkowski theory obtains increasing attention when \(p<1\). Two major open problems in this field are the so-called conjectured \(\log\)-Brunn-Minkowski inequality and the conjectured \(\log\)-Minkowski inequality. In the present paper, the authors define the \(L_p\)-mixed affine surface area probability measure and establish the \(\log\)-Minkowski inequalities for non-symmetric convex bodies of \(L_p\)-mixed affine surface area. The idea used in this paper is inspired by the work of \textit{A. Stancu} [Adv. Appl. Math. 73, 43--58 (2016; Zbl 1331.52014)].
reviewed by: Niufa Fang
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A39
zbMATH DE Number: 7382086
zbMATH Keywords: \(L_p\)-mixed affine surface area probability measure
zbMATH Keywords: \(\log\)-Minkowski inequality
zbMATH Keywords: \(L_p\)-mixed affine surface area
zbMATH Keywords: functional inequality
MaRDI profile type: Publication
full work available at URL: s11117-020-00804-3
OpenAlex ID: W3120275257
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DOI: 10.1007/S11117-020-00804-3
description: scientific article; zbMATH DE number 7382086