Description
We explain the connection between the classical Lieb-Oxford inequality and multimarginal optimal transport with repulsive cost. We can see that the first order condition is linked with the Kantorovich potential, and we show, through a detailed analysis of the shape of the potentials, that if a minimizer exists, then it should be compactly supported, extending the case N=1 which was already settled by Lieb and Oxford in their original contribution.
This is a work in preparation with R. Lelotte (U. Paris-Dauphine)
