Abstract
Under a complete Ricci flow, we construct a coupling of two Brownian motions such that their $\mathcal{L}_0$-distance is a supermartingale. This recovers a result of Lott [J. Lott, Optimal transport and Perelman's reduced volume, Calc. Var. Partial Differential Equations 36 (2009), no. 1, 49–84.] on the monotonicity of $\mathcal{L}_0$-distance between heat distributions.
Citation
Takafumi Amaba. Kazumasa Kuwada. "A coupling of Brownian motions in the $\mathcal{L}_0$-geometry." Tohoku Math. J. (2) 70 (1) 139 - 174, 2018. https://doi.org/10.2748/tmj/1520564422
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