Orlicz–Legendre Ellipsoids

The Orlicz–Legendre ellipsoids, which are in the framework of emerging dual Orlicz Brunn–Minkowski theory, are introduced for the first time. They are in some sense dual to the recently found Orlicz–John ellipsoids, and have largely generalized the classical Legendre ellipsoid of inertia. Several ne...

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Veröffentlicht in:	The Journal of Geometric Analysis 2016-07, Vol.26 (3), p.2474-2502
Hauptverfasser:	Zou, Du, Xiong, Ge
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Fourier Analysis Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
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Zusammenfassung:	The Orlicz–Legendre ellipsoids, which are in the framework of emerging dual Orlicz Brunn–Minkowski theory, are introduced for the first time. They are in some sense dual to the recently found Orlicz–John ellipsoids, and have largely generalized the classical Legendre ellipsoid of inertia. Several new affine isoperimetric inequalities are established. The connection between the characterization of Orlicz–Legendre ellipsoids and isotropy of measures is demonstrated.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-015-9636-0