A coupling of Brownian motions in the ${\mathcal{L}}_0$-geometry

Takafumi Amaba, Kazumasa Kuwada

Under a complete Ricci flow, we construct a coupling of two Brownian motion such that their ${\mathcal{L}}_0$-distance is a supermartingale. This recovers a result of Lott [J. Lott,…