# Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows

@article{Gigli2015ConvergenceOP, title={Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows}, author={Nicola Gigli and A. Mondino and Giuseppe Savar'e}, journal={Proceedings of The London Mathematical Society}, year={2015}, volume={111}, pages={1071-1129} }

Aim of this paper is to discuss convergence of pointed metric measure spaces in absence of any compactness condition. We propose various definitions, show that all of them are equivalent and that for doubling spaces these are also equivalent to the well known measured-Gromov-Hausdorff convergence. Then we show that the curvature conditions $CD(K,\infty)$ and $RCD(K,\infty)$ are stable under this notion of convergence and that the heat flow passes to the limit as well, both in the Wassersteinâ€¦Â Expand

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