Duality and Heat flow
Functional Analysis
2025-02-13 v5 Metric Geometry
Probability
Abstract
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.
Cite
@article{arxiv.2403.15357,
title = {Duality and Heat flow},
author = {Dario Cordero-Erausquin and Nathael Gozlan and Shohei Nakamura and Hiroshi Tsuji},
journal= {arXiv preprint arXiv:2403.15357},
year = {2025}
}