Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2

Delve into the advanced mathematical concepts of optimal transportation and Monge Ampère type equations in this comprehensive lecture by G. De Philippis from Scuola Normale Superiore di Pisa, Italy. Explore key topics including the Merge problem, super differential, isoperimetric problem, parametric problem, probability measure, and eigenvalue concepts. Gain insights into the solution, definition, and proof of related theorems. Examine the intricacies of equality everywhere, constant speed maps, and variation in the context of these complex mathematical theories. This in-depth presentation is part of the School and Workshop on "Geometric Measure Theory and Optimal Transport" series, offering a rigorous exploration of cutting-edge mathematical principles.

Intro
Merge problem
Solution
Definition
Super differential
Theorem
Proof
Isoperimetric problem
Parametric problem
Probability measure
Eigenvalue
Equality everywhere
Map
Constant speed
Variation