TOPICS IN OPTIMAL TRANSPORTATION (Graduate Studies in Mathematics 58) By CÉDRIC VILLANI: 370 pp., US$59.00, ISBN 0-8218-3312-X (American Mathematical Society, Providence, RI, 2003)

By G. Burton. 2004

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Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions (2007, neutral): “See [1, 27, 52] for more on optimal transport maps.”
An L1 ergodic theorem with values in a non-positively curved space via a canonical barycenter map (2011, background): “X×X d(x, y)2 dν(x, y), where (μ1|μ2) denotes the set of all probability measures ν on X × X that project into μ1 and μ2 on the first and the second factor, respectively (see [8] for more details on this metric).”
Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model (2010, background): “We refer to [38] for comments and relations of these dual distances to optimal transport distances.”