Wilhelm Klingenberg
Summary: Necessary background in analysis (density functions and its push forward by a map of domains, convexity and the second derivative condition, Legendre transform, convex dual of a functional, and Jensen’s inequality), Monge minimization problem of transport for a continuous cost function c(x, y) with an example in one space dimension, the dual maximization problem due to Leonid Kantorovich, Brenier Theorem.