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On Brunn–Minkowski-Type Inequalities for Polar Bodies

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Abstract

In this paper we prove a Brunn–Minkowski-type inequality for the polar set of the \(p\)-sum of convex bodies, which generalizes previous results by Firey, and we show it has an equivalent multiplicative version. We also make some considerations for the polar set of the so-called difference body.

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Acknowledgments

The authors would like to strongly thank the anonymous referee for the very valuable comments and helpful suggestions. Supported by MINECO-FEDER project MTM2012-34037.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain

    María A. Hernández Cifre & Jesús Yepes Nicolás

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  1. María A. Hernández Cifre
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  2. Jesús Yepes Nicolás
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Correspondence to María A. Hernández Cifre.

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Communicated by Steven G. Krantz.

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Hernández Cifre, M.A., Yepes Nicolás, J. On Brunn–Minkowski-Type Inequalities for Polar Bodies. J Geom Anal 26, 143–155 (2016). https://doi.org/10.1007/s12220-014-9541-y

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  • DOI: https://doi.org/10.1007/s12220-014-9541-y

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