Lower dimensional ellipsoids of maximal volume in convex bodies

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Mathematical Inequalities Pub Date : 2022-01-01 DOI:10.7153/jmi-2022-16-16

Ai-jun Li, Yan-Min Zhang

引用次数: 0

Abstract

In this paper, we show that the volume of a k -dimensional ellipsoid in the convex body formed by centered isotropic measures on the unit sphere is no large than that of a k dimensional Ball of radius √ n(n+1)/k(k+1) . It generalizes the John theorem to the lower dimensional cases. Mathematics subject classification (2020): 52A40.

查看原文本刊更多论文

凸体中体积最大的低维椭球体

本文证明了单位球上由心向各向同性测度形成的凸体中k维椭球的体积不大于半径为√n(n+1)/k(k+1)的k维球的体积。它将约翰定理推广到低维情况。数学学科分类(2020):52A40。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Mathematical Inequalities MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.90

自引率

3.40%

发文量

审稿时长

6-12 weeks

期刊介绍： The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts. ''JMI'' is published quarterly; in March, June, September, and December.