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A Functional Busemann Intersection Inequality

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Abstract

The Busemann intersection inequality states that if K is a compact domain in \({\mathbb {R}}^n\) then

where \(c(n)>0\) is an explicit constant, with equality if and only if K is an ellipsoid centered at the origin. In this paper, we prove a functional version of the Busemann intersection inequality. We also demonstrate an “equivalent” sharp entropy inequality for dual mixed volumes of functions.

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Acknowledgements

The author is very grateful to the referee for his/her careful reading and valuable suggestions and comments on previous versions of this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou, 215500, China

    Songjun Lv

  2. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Songjun Lv

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  1. Songjun Lv
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Correspondence to Songjun Lv.

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Research supported partly by Natural Science Foundation of Chongqing China under Grants cstc2018jcyjAX0190.

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Lv, S. A Functional Busemann Intersection Inequality. J Geom Anal 31, 6274–6291 (2021). https://doi.org/10.1007/s12220-020-00527-7

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  • DOI: https://doi.org/10.1007/s12220-020-00527-7

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