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Hölder continuity and injectivity of optimal maps
Alessio Figalli, Young-Heon Kim, Robert J. McCann
Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth…
Five lectures on optimal transportation: Geometry, regularity and applications
Nestor Guillen, Robert McCann
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost f…
Regularity of optimal transport maps on multiple products of spheres
Alessio Figalli, Young-Heon Kim, Robert J. McCann
This article addresses regularity of optimal transport maps for cost="squared distance" on Riemannian manifolds that are products of arbitrarily many round spheres with arbitrary s…