On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of $$\mathsf{RCD}^*(K,N)$$RCD∗(K,N) Metric Measure Spaces

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Well posedness of Lagrangian flows and continuity equations in metric measure spaces (2014, result): “ see Theorem 5.4. In particular, these hold assuming an abstract curvature lower bound on the underlying space, as discussed in Section 6, where we crucially exploit the recent results in [Sav13] and [AMS13] to show that our structural assumptions on Pand on A are fulﬁlled in the presence of lower b”
The globalization theorem for the Curvature-Dimension condition (2016, background): “Kuwada–Sturm [35, Corollary 3.13, Theorem 3.14 and Remark 3.26] for an extension to the essentially non-branching setting, cf. [67, 29]). Let us also mention here the work of Ambrosio–Mondino–Savar´e [10], who independently of a similar result in [35], established the local-to-global property for RC”