# Extremality, uniqueness and optimality of transference plans.

## Meeting Details

Abstract: For the transportation problem $\inf \int c(x,y) \pi$ where $\pi$ (the transference plan) is a probability measure with given marginals, and $c$ is a Borel cost, we are interested in the characterization of the minimizers (optimal plans). Analogous problems are the characterization of extremal points of the set of transference plans and its uniqueness. Even if the result is measure theoretic, it has applications to the solution of the Monge problem (existence of an optimal map) for convex l.s.c. costs.