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brenier potentials 1john domains 1log-concave densities 1optimal transport 1stability analysis 1Wasserstein distance 1

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math.AP2026

Gluing methods for quantitative stability of optimal transport maps

Cyril Letrouit, Quentin Mérigot

The paper proves that the optimal quadratic transport map from a fixed density to a varying measure depends bi‑Hölder continuously on the target measure, establishing quantitative…