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Mixed volumes and measures of asymmetry

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Abstract

The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry. In this paper, we first reveal a close connection between the L p -mixed volumes proposed by E. Lutwak and the p-measures of asymmetry, which have the Minkowski measure as a special case, introduced by Q. Guo. Then, a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R. J. Gardner, D. Hug and W. Weil recently, which is an extension of the p-measures.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University of Science and Technology, Suzhou, 215009, P. R. China

    Hai Lin Jin & Qi Guo

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Hai Lin Jin & Gang Song Leng

Authors
  1. Hai Lin Jin
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  2. Gang Song Leng
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  3. Qi Guo
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Correspondence to Hai Lin Jin.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11271244 and 11271282)

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Jin, H.L., Leng, G.S. & Guo, Q. Mixed volumes and measures of asymmetry. Acta. Math. Sin.-English Ser. 30, 1905–1916 (2014). https://doi.org/10.1007/s10114-014-3502-z

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  • DOI: https://doi.org/10.1007/s10114-014-3502-z

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