Mathematics – Classical Analysis and ODEs
Scientific paper
2010-09-17
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.
Ohta Shin-ichi
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