On the Lipschitz Properties of Transportation Along Heat Flows

2022/01/04 by Dan Mikulincer, Yair Shenfeld, Mikulincer, Dan +1 · 6 citations
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Point processes and geometric inequalities

paper · pdf · doi:10.1007/978-3-031-26300-2_9

Abstract

We prove new Lipschitz properties for transport maps along heat flows, constructed by Kim and Milman. For (semi)-log-concave measures and Gaussian mixtures, our bounds have several applications: eigenvalues comparisons, dimensional functional inequalities, and domination of distribution functions.

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