34 citations · 146 across the 31 of their papers we have counts for
4 papers · 1 filter
Regularity of optimal transportation between spaces with different dimensions
Brendan Pass
We study the regularity of solutions to an optimal transportation problem where the dimension of the source is larger than that of the target. We demonstrate that if the target is…
Uniqueness and Monge solutions in the multi-marginal optimal transportation problem
Brendan Pass
We study a multi-marginal optimal transportation problem. Under certain conditions on the cost function and the first marginal, we prove that the solution to the relaxed, Kantorovi…
On the local structure of optimal measures in the multi-marginal optimal transportation problem
Brendan Pass
We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of t…
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-…