EYAWKA5GI - Everything You Always Wanted to Know About the 5-Gradients-Inequality

par FILIPPO SANTAMBROGIO (Institut Camille Jordan, UCBL)

mercredi 3 déc. 2025, 10:00 → 12:00 Europe/Paris

125 (Braconnier)

The so-called "five-gradients-inequality" is a magical inequality involving the gradients of two densites on R^d, of the corresponding Kantorovich potentials, and on a fifth function, an arbitrary convex function on R^d. In this talk I plan to present

• several different proofs of this inequality, the original one which we established with De Philippis, Mészáros and Velichkov, but also the recent one by Caillet as well as one by Di Marino, Murro and Radici which also applies to the case of Riemannian manifolds with a curvature-dependent extra term
• the connections which hold in a very particular case with the geodesic convexity of the entropy
• various applications: BV bounds fro projections, for the JKO scheme, bounds on the Fisher information...