Orlicz–John ellipsoids

The Orlicz–John ellipsoids, which are in the framework of the booming Orlicz Brunn–Minkowski theory, are introduced for the first time. It turns out that they are generalizations of the classical John ellipsoid and the evolved Lp John ellipsoids. The analog of Ball's volume-ratio inequality is...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 265; pp. 132 - 168
Main Authors Zou, Du, Xiong, Ge
Format Journal Article
LanguageEnglish
Published Elsevier Inc 10.11.2014
Subjects
[formula omitted] John ellipsoids
Isotropy
Orlicz Brunn–Minkowski theory
Isotropy
52A40
Orlicz Brunn–Minkowski theory
Lp John ellipsoids
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Summary:The Orlicz–John ellipsoids, which are in the framework of the booming Orlicz Brunn–Minkowski theory, are introduced for the first time. It turns out that they are generalizations of the classical John ellipsoid and the evolved Lp John ellipsoids. The analog of Ball's volume-ratio inequality is established for the new Orlicz–John ellipsoids. The connection between the isotropy of measures and the characterization of Orlicz–John ellipsoids is demonstrated.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2014.07.034