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Duality and Heat flow

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arxiv 2403.15357 v5 pith:BDAR4R52 submitted 2024-03-22 math.FA math.MGmath.PR

Dario Cordero-Erausquin , Nathael Gozlan , Shohei Nakamura , Hiroshi Tsuji This is my paper · ORCID
classification math.FAmath.MGmath.PR
keywords flowheatinequalityappliesblaschke-santaloconvexdescribeduality
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We reveal the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke-Santalo inequality. We also describe local maximizers in this inequality.

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  1. $L^p$-Legendre Transforms and Mahler integrals: Asymptotics and the Fokker--Planck heat flow

    math.FA 2024-11 conditional novelty 6.0 of 10

    Introduces the L^p-Legendre transform and proves a functional L^p-Santaló inequality: after translation by the L^p-Santaló point, the L^p-Mahler integral of any convex function is bounded by that of the Gaussian |x|^2/2.

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