Submitted Paper
Inserted: 13 oct 2026
Last Updated: 13 oct 2026
Year: 2026
Abstract:
Controlling the $\infty-$Wasserstein distance by the $p-$Wasserstein distance is interesting both for theoretical and numerical applications. Previous works established this type of inequality for costs that increase with the distance. In this paper we prove an analogous inequality for optimal transport problems with pointwise costs given by a decreasing function of the distance. In particular, we present a general framework that encompasses the known cases and covers repulsive costs.
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