Introduzione alla geometria del trasporto ottimale con qualche applicazione alla fluidodinamica

Proof of the existence of an optimal plan. Proof of the existence of a pair of lower semicontinous convex conjugate functions which solves the Kantorovich problem. Proof of Knott-smith optimality criteria. Proof of Brenier theorem. Showing identical formulation between Euler equations and geodetics in Arnold’s work.