Optimal transport : old and new
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. Th...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2009. |
| Colección: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
338 |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Description d'après consultation du 26 mars 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Optimal transport, old and new, Cédric Villani, 2009, Berlin, Springer, 1 vol. (XXII-973 p.), Grundlehren der mathematischen Wissenschaften, 978-3-540-71049-3 • Optimal Transport, Texte imprimé, 9783540867456 • Optimal transport, old and new, Cédric Villani, 2009, Berlin, Springer, 1 vol. (XXII-973 p.), Grundlehren der mathematischen Wissenschaften, 978-3-540-71049-3 • Optimal transport, old and new, Cédric Villani, 2009, Berlin, Springer, 1 vol. (XXII-973 p.), Grundlehren der mathematischen Wissenschaften, 978-3-540-71049-3 |
Tabla de Contenidos:
- Couplings and changes of variables Three examples of coupling techniques The founding fathers of optimal transport Qualitative description of optimal transport Basic properties Cyclical monotonicity and Kantorovich duality The Wasserstein distances Displacement interpolation The Monge Mather shortening principle Solution of the Monge problem I: global approach Solution of the Monge problem II: Local approach The Jacobian equation Smoothness Qualitative picture Optimal transport and Riemannian geometry Ricci curvature Otto calculus Displacement convexity I Displacement convexity II Volume control Density control and local regularity Infinitesimal displacement convexity Isoperimetric-type inequalities Concentration inequalities Gradient flows I Gradient flows II: Qualitative properties Gradient flows III: Functional inequalities Synthetic treatment of Ricci curvature Analytic and synthetic points of view Convergence of metric-measure spaces Stability of optimal transport Weak Ricci curvature bounds I: Definition and Stability Weak Ricci curvature bounds II: Geometric and analytic properties