Tohoku Mathematical Journal
2018
March
SECOND SERIES VOL. 70, NO. 1

Tohoku Math. J.
70 (2018), 139-174

Title A COUPLING OF BROWNIAN MOTIONS IN THE $\MATHCAL{L}_{0}$-GEOMETRY

Author Takafumi Amaba and Kazumasa Kuwada

(Received April 28, 2015)
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.

Mathematics Subject Classification. Primary 53C21; Secondary 53C44, 58J65, 60J05.
Key words and phrases. $\mathcal{L}_0$-geometry, coupling of Brownian motions, approximation by geodesic random walks.

To the top of this page

Back to the Contents