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Pré-Publication, Document De Travail Année : 2023

TRANSPORT-ENTROPY FORMS OF DIRECT AND CONVERSE BLASCHKE-SANTALÓ INEQUALITIES

Résumé

We explore alternative functional or transport-entropy formulations of the Blaschke- Santaló inequality and of its conjectured counterpart due to Mahler. In particular, we obtain new direct and reverse 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. Finally, we show that the Mahler’s conjecture is equivalent to some reinforced log-Sobolev type inequality on the sphere.
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Dates et versions

hal-04154869 , version 1 (07-07-2023)

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Matthieu Fradelizi, Nathael Gozlan, Shay Sadovsky, Simon Zugmeyer. TRANSPORT-ENTROPY FORMS OF DIRECT AND CONVERSE BLASCHKE-SANTALÓ INEQUALITIES. 2023. ⟨hal-04154869⟩
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