A geometric approach to apriori estimates for optimal transport maps
数学专题报告
报告题目(Title)：A geometric approach to apriori estimates for optimal transport maps
报告人(Speaker)：Robert McCann (University of Toronto)
地点(Place)：ZOOM ID: 932 8426 6467 Passcode: 417967
时间(Time)：2026年3月27日（周五）9:30-10:30
邀请人(Inviter)：熊金钢
报告摘要
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.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
