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arXiv · 2201.01382

On the Lipschitz properties of transportation along heat flows

Dan Mikulincer·Yair Shenfeld
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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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Dan Mikulincer, Yair Shenfeld. 2022-01-04. On the Lipschitz properties of transportation along heat flows. https://doi.org/10.1007/978-3-031-26300-2_9

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