14 citations · 23 across the 4 of their papers we have counts for
3 papers · 1 filter
Optimal transportation, topology and uniqueness
Najma Ahmad, Hwa Kil Kim, Robert J. McCann
The Monge-Kantorovich transportation problem involves optimizing with respect to a given a cost function. Uniqueness is a fundamental open question about which little is known when…
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…
Extremal doubly stochastic measures and optimal transportation
Najma Ahmad, Hwa Kil Kim, Robert J. McCann
This article connects the theory of extremal doubly stochastic measures to the geometry and topology of optimal transportation. We begin by reviewing an old question (# 111) of Bir…