@Misc{ gigc, author = { Gigli, Nicola }, title = { On the inverse implication of Brenier-McCann theorems and the structure of $(P_2(M),W_2)$ }, journal = { Meth. Appl. of Anal. }, year = { 2009 }, pages = { }, URL = { http://cvgmt.sns.it/paper/983/ }, note = { cvgmt preprint} }