Optimal Transport and Applications to Geometric Optics

Dr. Cristian E. Gutierrez is a Professor at Temple University. His research areas include partial differential equations, geometric optics, optimal transport, and electromagnetism. He is a Fellow of the American Mathematical Society, a Member of the Academy of Sciences of Argentina, and a Member of the Academy of Sciences of the University of Bologna, Italy.

• Chapter 1 Introduction.- Chapter 2 The normal mapping or subdifferential.-Chapter 3 Sinkhorn’s theorem and application to the distribution problem.- Chapter4 Monge-Kantorovich distance.- Chapter 5 Multivalued measure preserving maps.- Chapter 6 Kantorovich Dual Problem.- Chapter 7 Brenier and Aleksandrov solutions.- Chapter 8 Cyclical monotonicity.- Chapter 9 Quadratic cost.- Chapter 10 Brenier ’s Polar Factorization Theorem.- Chapter 11 Benamou and Brenier formula.- Chapter 12 Snell’s law of refraction.- Chapter 13 Solution of the far field refractor problem < 1.- Chapter 14 Proof of the Disintegration Theorem.- Chapter 15 Acknowledgements.- Chapter 16 References.

"This book gives a comprehensible presentation which covers several important topics on optimal transport in a concise yet detailed way. … Its succinct style of presentation makes this book suitable for an introductory graduate-level course on optimal transport, or, with appropriate selection of topics, for a summer school on optimal transport. Additionally, it serves as a valuable reference for researchers who plan to apply optimal transport theory in their work." (Henok Mawi, Mathematical Reviews, February, 2025)