ON LEGENDRE AND LYZ ZELLIPSOIDS  

作　　者：Xinbao LU Ge XIONGG Jiangyan TAO 鲁新宝;熊革;陶江艳(School of Mathematical Sciences,Key Laboratory of Intelligent Computing and Applications(Ministry of Education),Tongji University,Shanghai,200092,China)

机构地区：[1]School of Mathematical Sciences,Key Laboratory of Intelligent Computing and Applications(Ministry of Education),Tongji University,Shanghai,200092,China

出　　处：《Acta Mathematica Scientia》2025年第1期180-188,共9页数学物理学报(B辑英文版)

基　　金：supported by the NSFC(12271407).

摘　　要：We study the Legendre ellipsoid and the LYZ ellipsoid.First,we give a direct proof of the Cramer-Rao inequality for convex bodies.Second,we prove that origin-centered ellipsoids are the only convex bodies with identical Löwner and Legendre ellipsoids.Finally,we establish a mean width inequality for convex bodies whose LYZ ellipsoids are the Euclidean unit ball.

关 键 词：Legendre ellipsoid LYZ ellipsoid Lowner ellipsoid 

分 类 号：O17[理学—数学]