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Orlicz–Legendre Ellipsoids

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Abstract

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.

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Acknowledgments

We are grateful to the referee(s) for many suggested improvements and for the thoughtful and careful reading given to the original draft of this paper. Research of the authors was supported by NSFC No. 11471206.

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  1. Department of Mathematics, Wuhan University of Science and Technology, Wuhan, 430081, People’s Republic of China

    Du Zou

  2. Department of Mathematics, Tongji University, Shanghai, 200092, People’s Republic of China

    Ge Xiong

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  1. Du Zou
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  2. Ge Xiong
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Correspondence to Ge Xiong.

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Zou, D., Xiong, G. Orlicz–Legendre Ellipsoids. J Geom Anal 26, 2474–2502 (2016). https://doi.org/10.1007/s12220-015-9636-0

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  • DOI: https://doi.org/10.1007/s12220-015-9636-0

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