Calculus of Variations and Geometric Measure Theory
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M. Colombo - M. Fathi

Bounds on optimal transport maps onto log-concave measures

created by colombom on 20 Oct 2019
modified on 25 Oct 2019



Inserted: 20 oct 2019
Last Updated: 25 oct 2019

Year: 2019
Links: Arxiv PDF


We consider strictly log-concave measures, whose bounds degenerate at infinity. We prove that the optimal transport map from the Gaussian onto such a measure is locally Lipschitz, and that the eigenvalues of its Jacobian have controlled growth at infinity.

Keywords: Optimal transport, log-concave measure

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