Before revision: Inspired by the matching of supply to demand in logistical problems, the optimal transportation (or Monge-Kantorovich ) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.
After revision: Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich ) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.