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Some logarithmic Minkowski inequalities for nonsymmetric convex bodies

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Abstract

We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other inequalities are obtained.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11671325 and 11401486) and the Natural Science Foundation Project of CQ CSTC (Grant No. cstc2016jcyjA0465). Authors thank referees for comments and suggestions that directly lead to improvement of the original manuscript. The corresponding author thanks Professor G. Zhang and Dr. G. Zhu for valuable suggestions and discussions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    XingXing Wang, WenXue Xu & JiaZu Zhou

  2. Southwest Guizhou Vocational College of Technology for Nationalities, Kaili, 556000, China

    JiaZu Zhou

Authors
  1. XingXing Wang
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  2. WenXue Xu
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  3. JiaZu Zhou
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Correspondence to JiaZu Zhou.

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Wang, X., Xu, W. & Zhou, J. Some logarithmic Minkowski inequalities for nonsymmetric convex bodies. Sci. China Math. 60, 1857–1872 (2017). https://doi.org/10.1007/s11425-016-9056-5

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  • DOI: https://doi.org/10.1007/s11425-016-9056-5

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