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On optimal transport maps between d1-concave densities
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On optimal transport maps between d1-concave densities
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On optimal transport maps between d1-concave densities
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Journal Article
On optimal transport maps between d1-concave densities
2026
Overview
In this paper we extend the scope of Caffarelli’s contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in Rd. Our focus is on a broader category of densities, specifically those that are d1-concave and can be represented as V−d, where V is convex. By setting appropriate conditions, we derive linear or sublinear limitations for the optimal transport map. This leads us to a comprehensive Lipschitz estimate that aligns with the principles established in Caffarelli’s theorem.
Publisher
European Mathematical Society (EMS)
Subject
