Accepted Paper

Inserted: 5 apr 2024
Last Updated: 7 oct 2024

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Year: 2024

Abstract:

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 $\mathbb{R}^d$. Our focus is on a broader category of densities, specifically those that are $1/d$-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.

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