Communications in Analysis and Geometry

Volume 22 (2014)

Number 2

A simple method for the optimal transportation

Pages: 371 – 386

DOI: http://dx.doi.org/10.4310/CAG.2014.v22.n2.a7

Author

Xian-Tao Huang (School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou, China)

Abstract

In this paper, we will give a new proof of the monotonicity of Wasserstein distances of two diffusions under super Ricci flow. Our proof is based on the coupling method of B. Andrew and J. Clutterbuck. The same method can also be applied to the contractivity of normalized $\mathit{L}$-Wasserstein distance under backward Ricci flow.

Full Text (PDF format)