On the degeneracy of optimal transportation

Abstract

We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that satisfy the curvature condition of Ma, Trudinger, and Wang.

arXiv comment33 pages

References in corpus (1)

• An iterative scheme for solving the optimal transportation problem

Cited by in corpus (1)

• The local geometry of maps with c-convex potentials