# Metric measure spaces with Riemannian Ricci curvature bounded from below

@article{Ambrosio2014MetricMS, title={Metric measure spaces with Riemannian Ricci curvature bounded from below}, author={Luigi Ambrosio and Nicola Gigli and Giuseppe Savar'e}, journal={Duke Mathematical Journal}, year={2014}, volume={163}, pages={1405-1490} }

In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries. It can be given in terms of an enforcement of the Lott, Sturm and Villani geodesic convexity condition for the entropy coupled with the linearity of the heat flow. Besides stability, it enjoys the same tensorization, global-to-local and local-to-global properties. In these spaces, that…

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