Ricci curvature, entropy and optimal transport
نویسنده
چکیده
This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability measures characterizes lower bounds of the Ricci curvature. We then discuss geometric properties of general metric measure spaces satisfying this convexity condition. Mathematics Subject Classification (2000): 53C21, 53C23, 53C60, 28A33, 28D20
منابع مشابه
Ricci curvature , entropy and optimal transport – Summer School in Grenoble 2009 – ‘ Optimal Transportation : Theory and Applications
These notes are the planned contents of my lectures. Some parts could be only briefly explained or skipped due to the lack of time or possible overlap with other lectures. The aim of these lectures is to review the recent development on the relation between optimal transport theory and Riemannian geometry. Ricci curvature is the key ingredient. Optimal transport theory provides a good character...
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تاریخ انتشار 2017