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Stability of some versions of the Prékopa–Leindler inequality

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Abstract

Two consequences of the stability version of the one dimensional Prékopa–Leindler inequality are presented. One is the stability version of the Blaschke–Santaló inequality, and the other is a stability version of the Prékopa– Leindler inequality for even functions in higher dimensions, where a recent stability version of the Brunn–Minkowski inequality is also used in an essential way.

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Authors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Keith M. Ball

  2. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Károly J. Böröczky

  3. Universitat Politècnica de Catalunya, Barcelona Tech, Barcelona, Spain

    Károly J. Böröczky

  4. Department of Geometry, Roland Eötvös University, Budapest, Hungary

    Károly J. Böröczky

Authors
  1. Keith M. Ball
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  2. Károly J. Böröczky
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Corresponding author

Correspondence to Károly J. Böröczky.

Additional information

K. J. Böröczky was Supported by OTKA grants 068398 and 75016, and by the EU Marie Curie TOK project DiscConvGeo, and FP7 IEF grant GEOSUMSETS.

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Ball, K.M., Böröczky, K.J. Stability of some versions of the Prékopa–Leindler inequality. Monatsh Math 163, 1–14 (2011). https://doi.org/10.1007/s00605-010-0222-z

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  • DOI: https://doi.org/10.1007/s00605-010-0222-z

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