On the Lipschitz properties of transportation along heat flows
arXiv:2201.01382 · 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.
Erroneous dimensional log-Sobolev inequality results removed. Bounds in Theorem 1 and Theorem 2 improved, and optimality of Theorem 2 about Gaussian mixtures established. Discussion on relation to Brownian transport map removed