JournalsrmiVol. 40, No. 5pp. 1917–1952

Transport-entropy and functional forms of Blaschke–Santaló inequalities

  • Matthieu Fradelizi

    Université Gustave Eiffel, Université Paris Est Creteil, CNRS, LAMA UMR8050, Marne-la-Vallée, France

  • Nathaël Gozlan

    Université Paris Cité, Paris, France

  • Shay Sadovsky

    Tel Aviv University, Tel Aviv, Israel

  • Simon Zugmeyer

    ENS de Lyon, UMPA (UMR 5669), Lyon, France
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Abstract

We explore alternative functional or transport-entropy formulations of the Blaschke–Santaló inequality. In particular, we obtain new Blaschke–Santaló inequalities for -concave functions. We also obtain new sharp symmetrized transport-entropy inequalities for a large class of spherically invariant probability measures, including the uniform measure on the unit Euclidean sphere and generalized Cauchy and Barenblatt distributions.

Cite this article

Matthieu Fradelizi, Nathaël Gozlan, Shay Sadovsky, Simon Zugmeyer, Transport-entropy and functional forms of Blaschke–Santaló inequalities. Rev. Mat. Iberoam. 40 (2024), no. 5, pp. 1917–1952

DOI 10.4171/RMI/1490