67 citations · 313 across the 39 of their papers we have counts for
4 papers · 2 filters
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…
Hölder continuity for optimal multivalued mappings
Robert J. McCann, Maria Sosio
Gangbo and McCann showed that optimal transportation between hypersurfaces generally leads to multivalued optimal maps - bivalent when the target surface is strictly convex. In thi…
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…
Rectifiability of Optimal Transportation Plans
Robert J. McCann, Brendan Pass, Micah Warren
The purpose of this note is to show that the solution to the Kantorovich optimal transportation problem is supported on a Lipschitz manifold, provided the cost is with non-…