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Volume inequalities for Orlicz mean bodies

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Abstract

In this paper, the Orlicz mean body H ϕ K of a convex body K is introduced. Using the notion of shadow system, we establish a sharp lower estimate for the volume ratio of H ϕ K and K.

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Acknowledgement

The authors are grateful to the anonymous referees for their careful reading and many valuable suggestions, which has improved the paper greatly. The authors are supported in part by the National Natural Science Foundation of China (11271244) and in part by Science and Technology Key Project of the Education Department of Henan Province (14A110005).

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    CHANGMIN DU & GANGSONG LENG

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    LUJUN GUO

Authors
  1. CHANGMIN DU
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  2. LUJUN GUO
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  3. GANGSONG LENG
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Correspondence to CHANGMIN DU.

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Communicating Editor: B V Rajarama Bhat

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DU, C., GUO, L. & LENG, G. Volume inequalities for Orlicz mean bodies. Proc Math Sci 125, 57–70 (2015). https://doi.org/10.1007/s12044-015-0214-y

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  • DOI: https://doi.org/10.1007/s12044-015-0214-y

Keywords

2010 Mathematics Subject Classification

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