New article ideas

Below, you can find a list of new article ideas and suggested references. (Feel free to incorporate additional references! Please list all references you use at the bottom of your article.) If you choose to write about one of these ideas, remove it from the list below and create a new link on the main page.

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The Optimal Transport Problem

• Monge Problem (for general costs); Villani (3-4, 6-9), Santambrogio (xiv-xvii,1-9)
• Kantorovich Problem (for general costs); Villani (1-3, 6-9), Santambrogio (xv-xvii,1-9)
• Discrete Optimal Transport (for general costs); Villani (5)
• Kantorovich Dual Problem (for general costs); Villani (17-21), Santambrogio (9-16)
• Kantorovich Dual Problem (for $c(x,y)=d(x,y)$ where $d$ is a metric); Villani (34)
• Kantorovich Dual Problem (for $c(x,y)=d(x,y)^{2}$ where $d$ is a metric); Santambrogio (16-18)
• Optimal Transport and the Monge Ampère equation; Santambrogio (xvi, 54-57)
• Prokhorov's Theorem and Compactness of Transport Plans (Katy will add refs)