Pré-Publication, Document De Travail Année : 2025

Stability of optimal transport maps on Riemannian manifolds

Résumé

We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure ρ under variations of the target measure µ, when the cost function is the squared Riemannian distance on a Riemannian manifold. Previous works were restricted to subsets of Euclidean spaces, or made specific assumptions either on the manifold, or on the regularity of the transport maps. Our proof techniques combine entropyregularized optimal transport with spectral and integral-geometric techniques. As some of the arguments do not rely on the Riemannian structure, our work also paves the way towards understanding stability of optimal transport in more general geometric spaces.

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hal-05029965 , version 1 (10-04-2025)

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  • HAL Id : hal-05029965 , version 1

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Jun Kitagawa, Cyril Letrouit, Quentin Merigot. Stability of optimal transport maps on Riemannian manifolds. 2025. ⟨hal-05029965⟩
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