Transport-entropy and functional forms of Blaschke–Santaló inequalities
Matthieu Fradelizi
Université Gustave Eiffel, Université Paris Est Creteil, CNRS, LAMA UMR8050, Marne-la-Vallée, FranceNathaël Gozlan
Université Paris Cité, Paris, FranceShay Sadovsky
Tel Aviv University, Tel Aviv, IsraelSimon 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. (2024), published online first
DOI 10.4171/RMI/1490