Optimal Transportation and Applications
timetable:
Thu 5 Dec, 11:10 - 11:55, Aula Dini
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A geometric approach to apriori estimates for optimal transport maps
speaker: Robert McCann (University of Toronto)abstract: A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma-Trudinger-Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior modulus of the differential estimate for smooth optimal maps. We describe a new derivation of this estimate with Brendle, Leger and Rankin which relies in part on Kim, McCann and Warren's observation that the graph of an optimal map becomes a volume maximizing spacelike submanifold when the product of the source and target domains is endowed with a suitable pseudo-Riemannian geometry that combines both the marginal densities and the cost.
timetable:
Thu 5 Dec, 11:10 - 11:55, Aula Dini
<< Go back