Coarse Ricci curvature as a function on \({M\times M}\) (Q681236)
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| Language | Label | Description | Also known as |
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| English | Coarse Ricci curvature as a function on \({M\times M}\) |
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Coarse Ricci curvature as a function on \({M\times M}\) (English)
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30 January 2018
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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.
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Ricci curvature
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metric measure space
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discrete metric space
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metric geometry
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