Ricci curvature, entropy and optimal transport

Details Ricci curvature, entropy and optimal transport Ricci curvature, entropy and optimal transport

2010-09-17

arxiv.org/abs/1009.3431v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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