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Extensions of Reverse Volume Difference Inequalities

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Analytic Aspects of Convexity

Part of the book series: Springer INdAM Series ((SINDAMS,volume 25))

Abstract

Volume difference inequalities are designed to estimate the difference between volumes of two bodies in terms of the maximal or minimal difference between areas of sections of these bodies. In this note we extend two such inequalities established in Koldobsky (Adv Math 283:473–488, 2015) and Giannopoulos and Koldobsky (Trans Am Math Soc, https://doi.org/10.1090/tran/7173, to appear) from the hyperplane case to the case of sections of arbitrary dimensions.

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Acknowledgements

The first named author was supported in part by the US National Science Foundation grant DMS-1700036. The second named author was partially supported by Fundamental Research Funds for the Central Universities (No. XDJK2016D026) and China Scholarship Council.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, USA

    Alexander Koldobsky & Denghui Wu

  2. School of Mathematics and Statistics, Southwest University, Chongqing, China

    Denghui Wu

Authors
  1. Alexander Koldobsky
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  2. Denghui Wu
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Corresponding author

Correspondence to Alexander Koldobsky .

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Editors and Affiliations

  1. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Gabriele Bianchi

  2. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Andrea Colesanti

  3. Dept. of Mathematics and Computer Science “U. Dini”, University of Florence, Florence, Italy

    Paolo Gronchi

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Koldobsky, A., Wu, D. (2018). Extensions of Reverse Volume Difference Inequalities. In: Bianchi, G., Colesanti, A., Gronchi, P. (eds) Analytic Aspects of Convexity. Springer INdAM Series, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-71834-7_4

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