On the velocities of flows consisting of cyclically monotone maps A. Tudorascu 35M1049J4082C99flows of mapscyclically monotone mapsoptimal mass transportWasserstein metricoptimal mapsvelocities of absolutely continuous curves Motivated by work on one-dimensional Euler-Poisson systems, Gangbo et al. proved a surprisingly general flow-map formula which unequivocally links an absolutely continuous curve in the Wasserstein space to the corresponding family of optimal maps pushing forward a given reference measure to each measure on the curve. In this work we prove a similar result for higher dimensions. Possible applications to variational solutions for pressureless gas dynamics systems are discussed. These solutions are obtained as absolutely continuous curves in a new metric space which is topologically equivalent to the Wasserstein space. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3955 10.1512/iumj.2010.59.3955 en Indiana Univ. Math. J. 59 (2010) 929 - 956 state-of-the-art mathematics http://iumj.org/access/