Optimal Transport

Old and New

  • Cédric Villani

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 338)

Table of contents

  1. Front Matter
    Pages I-XXII
  2. Introduction

    1. Front Matter
      Pages 1-3
    2. Cédric Villani
      Pages 5-20
    3. Cédric Villani
      Pages 21-28
    4. Cédric Villani
      Pages 29-37
  3. Qualitative description of optimal transport

    1. Front Matter
      Pages 39-41
    2. Cédric Villani
      Pages 43-49
    3. Cédric Villani
      Pages 51-92
    4. Cédric Villani
      Pages 93-111
    5. Cédric Villani
      Pages 113-162
    6. Cédric Villani
      Pages 163-203
    7. Cédric Villani
      Pages 205-213
    8. Cédric Villani
      Pages 215-272
    9. Cédric Villani
      Pages 273-279
    10. Cédric Villani
      Pages 281-332
    11. Cédric Villani
      Pages 333-351
  4. Optimal transport and Riemannian geometry

    1. Front Matter
      Pages 353-356
    2. Cédric Villani
      Pages 357-420
    3. Cédric Villani
      Pages 421-433
    4. Cédric Villani
      Pages 435-447

About this book


At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results.

PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.



Monge-Kantorovich problem Optimal transport Riemannian geometry curvature dynamical systems

Authors and affiliations

  • Cédric Villani
    • 1
  1. 1.Unité de Mathématiques Pures t Appliquées (UMPA)École Normale Supérieure de LyonLyon CX 07France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71050-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71049-3
  • Online ISBN 978-3-540-71050-9
  • Series Print ISSN 0072-7830
  • About this book