ON LEGENDRE AND LYZ ELLIPSOIDS

ON LEGENDRE AND LYZ ELLIPSOIDS

ON LEGENDRE AND LYZ ELLIPSOIDS

ON LEGENDRE AND LYZ ELLIPSOIDS

ON LEGENDRE AND LYZ ELLIPSOIDS

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doi:10.1007/s10473-025-0114-x

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 180-188.doi: 10.1007/s10473-025-0114-x

Xinbao Lu¹, Ge Xiong^1,*, Jiangyan Tao²

1. School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai 200092, China;
2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2024-09-04 发布日期:2025-02-06
通讯作者: *Ge Xiong, E-mail,: xiongge@tongji.edu.cn
作者简介:Xinbao Lu, E-mail,: xinbaolu@tongji.edu.cn; Jiangyan Tao, E-mail,: taojiangyan@zjnu.edu.cn
基金资助:
Xiong's work was supported by the NSFC (12271407).

Xinbao Lu¹, Ge Xiong^1,*, Jiangyan Tao²

1. School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai 200092, China;
2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

Received:2024-09-04 Published:2025-02-06
Contact: *Ge Xiong, E-mail,: xiongge@tongji.edu.cn
About author:Xinbao Lu, E-mail,: xinbaolu@tongji.edu.cn; Jiangyan Tao, E-mail,: taojiangyan@zjnu.edu.cn
Supported by:
Xiong's work was 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, Löwner ellipsoid

Abstract: 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.

Key words: Legendre ellipsoid, LYZ ellipsoid, Löwner ellipsoid

中图分类号:

52A40

Xinbao Lu, Ge Xiong, Jiangyan Tao. ON LEGENDRE AND LYZ ELLIPSOIDS[J]. 数学物理学报(英文版), 2025, 45(1): 180-188.

Xinbao Lu, Ge Xiong, Jiangyan Tao. ON LEGENDRE AND LYZ ELLIPSOIDS[J]. Acta mathematica scientia,Series B, 2025, 45(1): 180-188.

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