Cone-Compatible Monge Geometry for High-Dimensional Ordered Optimal Transport

ArXi:2606.04695v1 Announce Type: new High-dimensional optimal transport is seldom available in closed form. The one-dimensional case is exceptional because the order of the real line is compatible with convex transport costs, making monotone rearrangement optimal. This paper studies when an analogous Monge structure can be recovered in higher dimensions from a partial order. We