From the 2 of 5 linked papers with an AI index.
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A Brenier-Strassen Theorem on CAT(kappa) Spaces
Nathael Gozlan, Hugo Malamut, Shin-Ichi Ohta
The paper generalizes the Brenier‑Strassen theorem to spaces with curvature bounded above, proving existence and uniqueness of a Wasserstein‑2 projection onto measures dominated in…
Global Regularity Estimates for Optimal Transport via Entropic Regularisation
Nathael Gozlan, Maxime Sylvestre
We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequal…
On the quadratic barycentric transport problem
Nathael Gozlan, Thibaut Le Gouic, Paul-Marie Samson
We investigate the structure of optimal transport plans, dual optimizers, and geodesic paths for the quadratic barycentric transport problem.
Duality and Heat flow
Dario Cordero-Erausquin, Nathael Gozlan, Shohei Nakamura +1
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 describ…
Weak optimal transport with unnormalized kernels
Philippe Choné, Nathael Gozlan, Francis Kramarz
We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions f…