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A Mixed Volumetry for the Anisotropic Logarithmic Potential

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Abstract

This paper is devoted to investigating a mixed volume from the anisotropic potential with natural logarithm as a better complement to the end point case of the most recently developed mixed volumes from the anisotropic Riesz-potential. An optimal polynomial \(\log \)-inequality is not only discovered but also applicable to produce a polynomial dual for the conjectured fundamental \(\log \)-Minkowski inequality in convex geometry analysis, whence generalizing the dual \(\log \)-Minkowski inequality for mixed volume of two star bodies.

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Acknowledgements

We are grateful not only for Han Hong’s comments on a possible application of the brand-new mixed volume to convex geometry, but also for the referee’s suggestions improving the paper. SH is supported by both CSC of China and NSERC of Canada. JX is supported by NSERC of Canada.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University, St. John’s, NL, A1C 5S7, Canada

    S. Hou & J. Xiao

  2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, Hebei, China

    S. Hou

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  1. S. Hou
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  2. J. Xiao
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Correspondence to J. Xiao.

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Hou, S., Xiao, J. A Mixed Volumetry for the Anisotropic Logarithmic Potential. J Geom Anal 28, 2028–2049 (2018). https://doi.org/10.1007/s12220-017-9895-z

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  • DOI: https://doi.org/10.1007/s12220-017-9895-z

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