Transport-entropy and functional forms of Blaschke–Santaló inequalities

• Matthieu Fradelizi ^[2] ; Nathaël Gozlan ^[3] ; Shay Sadovsky ^[1] ; Simon Zugmeyer ^[4]
  1. [1] Tel Aviv University

     Tel Aviv University

     Israel

     
  2. [2] Université Gustave Eiffel, Université Paris Est Creteil, CNRS, LAMA UMR8050, Marne-la-Vallée, France
  3. [3] Université Paris Cité, Paris, France
  4. [4] ENS de Lyon, UMPA (UMR 5669), Lyon, France

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 5, 2024, págs. 1917-1952
• Idioma: inglés
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• Resumen

  • We explore alternative functional or transport-entropy formulations of the Blaschke–Santaló inequality. In particular, we obtain new Blaschke–Santaló inequalities for s-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.