Comparison of transport map generated by heat flow interpolation and the optimal transport Brenier map

Abstract

This note shows that the non-expansive transport map constructed by Y.-H. Kim and E. Milman using heat flow interpolation is in general different from the optimal transport Brenier map.

5 pages

Cited by in corpus (2)

• On the Lipschitz properties of transportation along heat flows
• $L^{\infty }$-optimal transport of anisotropic log-concave measures and exponential convergence in Fisher's infinitesimal model