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DUAL $L_{p}$ JOHN ELLIPSOIDS

Published online by Cambridge University Press:  08 January 2008

Wuyang Yu ,
Gangsong Leng  and
Donghua Wu
Wuyang Yu
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China (yu\_wuyang@163.com; gleng@staff.shu.edu.cn; dhwu@staff.shu.edu.cn)
Gangsong Leng
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China (yu\_wuyang@163.com; gleng@staff.shu.edu.cn; dhwu@staff.shu.edu.cn)
Donghua Wu
Affiliation:
Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China (yu\_wuyang@163.com; gleng@staff.shu.edu.cn; dhwu@staff.shu.edu.cn)
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Abstract

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In this paper, the dual $L_p$ John ellipsoids, which include the classical Löwner ellipsoid and the Legendre ellipsoid, are studied. The dual $L_p$ versions of John's inclusion and Ball's volume-ratio inequality are shown. This insight allows for a unified view of some basic results in convex geometry and reveals further the amazing duality between Brunn–Minkowski theory and dual Brunn–Minkowski theory.

Keywords

Primary 52A3952A40Löwner ellipsoidLegendre ellipsoid$L_p$ John ellipsoiddual $L_p$ John ellipsoids
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 737 - 753
Copyright
Copyright © Edinburgh Mathematical Society 2007