Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds

Mathias Braun, Karen Habermann, Karl-Theodor Sturm

Given a metric measure space $(X,\mathsf{d},\mathfrak{m})$ and a lower semicontinuous, lower bounded function $k:X\to \mathbb{R}$, we prove the equivalence of the synthetic ap…