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cat(kappa) spaces 1convex order 1martingale transport 1metric geometry 1optimal transport 1

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math.FA2026

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…