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math.FA2026
Functional inequalities along Wasserstein geodesics
Nathael Gozlan, Hugo Malamut, Irène Waldspurger
We study functional inequalities along Wasserstein geodesics. If 0 and 1 are respectively 0 -and 1 -strongly log-concave probability measures on R n , we prove that…
math.FA2026
A Brenier-Strassen Theorem on CAT(kappa) Spaces
Nathael Gozlan, Hugo Malamut, Shin-Ichi Ohta
We extend the Brenier-Strassen theorem about projections in convex order to non-flat spaces with curvature bounded from above. Precisely, for probability measures , of finit…