Coarse Ricci curvature as a function on \({M\times M}\) (Q681236)

The authors propose an alternative notion of the coarse Ricci curvature on smooth metric measure spaces. In contrary to \textit{K.-T. Sturm}'s case [Acta Math. 196, No. 1, 65--131 (2006; Zbl 1105.53035); ibid. 196, No. 1, 133--177 (2006; Zbl 1106.53032)] which works in the case of length spaces and \textit{Y. Ollivier}'s idea [Adv. Stud. Pure Math. 57, 343--381 (2010; Zbl 1204.53035)] based on Markov processes, here the authors consider the ``iterated Carré du Champ'' introduced by \textit{D. Bakry} and \textit{M. Émery} [Lect. Notes Math. 1123, 177--206 (1985; Zbl 0561.60080)]. However, the main results are proved only for (smooth) Riemannian manifolds.