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- W2904573306 abstract "The goal of this work is to reach the comprehension of the proof of aremarkable result: Brenier's Polar Factorization Theorem.This theorem states that, whenever we have a map h from a bounded subset of R^n with positive Lebesgue measure, which satisfies some conditions it canbe decomposed. These conditions are that h needs to be L^2 vector-valued and nondegenerate, in a sense that we will explore here. The representation of h we achieve with this result is the composition of a rearrangement that is the gradiente a convex function, and a measure-preserving map.The main feature of Brenier regarding this problem was reading it as aproblem of Optimal transportation, specially using Kantorovich duality in avery smart way, even if his original motivations were completely out ofthis area. This is the reason why, first, we will dive a little into theworld of Optimal transportation reaching real important results asKantorovich duality and the Knott-Smith optimality criterion. In the end,instead, we will re-emerge from this field, and finally consider Brenier'spolar factorization theorem with its proof." @default.
- W2904573306 created "2018-12-22" @default.
- W2904573306 creator A5028908279 @default.
- W2904573306 date "2018-07-20" @default.
- W2904573306 modified "2023-09-26" @default.
- W2904573306 title "Brenier’s polar factorization theorem" @default.
- W2904573306 hasPublicationYear "2018" @default.
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