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Smoothness of optimal transport in curved geometry
Recent works of Ma-Trudinger-Wang and Loeper have revealed
an amazingly intimate connection between the regularity theory for
optimal transport, and a novel nonlocal notion of sectional curvature.
In this talk I shall summarize the state of the art and present
some new results about the geometric and analytic implications of
Ma-Trudinger-Wang curvature bounds, as well as their stability.
Some of these results have been obtained in collaboration with Loeper.
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