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Topics in Optimal Transportation

About this Title

Cédric Villani, École Normale Supérieure de Lyon, Lyon, France

Publication: Graduate Studies in Mathematics
Publication Year: 2003; Volume 58
ISBNs: 978-0-8218-3312-4 (print); 978-1-4704-1804-5 (online)
MathSciNet review: MR1964483
MSC: Primary 90-02; Secondary 28D05, 35B65, 35J60, 49N90, 49Q20, 90B20

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Table of Contents


  • Chapter 1. Introduction
  • Chapter 2. The Kantorovich duality
  • Chapter 3. Geometry of optimal transportation
  • Chapter 4. Brenier’s polar factorization theorem
  • Chapter 5. The Monge-Ampère equation
  • Chapter 6. Displacement interpolation and displacement convexity
  • Chapter 7. Geometric and Gaussian inequalities
  • Chapter 8. The metric side of optimal transportation
  • Chapter 9. A differential point of view on optimal transportation
  • Chapter 10. Entropy production and transportation inequalities
  • Chapter 11. Problems