Titlebook: Optimal Transport and Applications to Geometric Optics; Cristian E. Gutiérrez Book 2023 The Editor(s) (if applicable) and The Author(s), u

延期

豪華

變形

remission

Monge-Kantorovich Distance,This Chapter begins with the notion of disintegration of measures and states the disintegration theorem fully proved later in Chap. .. The Monge-Kantorovich or Wasserstein distance is introduced and its properties proved using disintegration.

記憶法

Lyme-disease

Kantorovich Dual Problem,The dual Kantorovich problem is introduced and it is proved, under aproppiate assumptions on the cost function, that this problem is equivalent to the Kantorovich and the Monge problems introduced in Chap. .. It is also proved the invertibility of optimal maps for the Monge problem.

平息

Cyclical Monotonicity,In this chapter the notion of cyclical monotonicity of multi-valued maps is analyzed.

analogous

令人發(fā)膩

,Brenier’s Polar Factorization Theorem,A detailed proof of Brenier’s theorem is given.

bibliophile