Villani, Cédric
Optimal Transport
1. Couplings and changes of variables
2. Three examples of coupling techniques
3. The founding fathers of optimal transport
I. Qualitative description of optimal transport
4. Basic properties
5. Cyclical monotonicity and Kantorovich duality
6. The Wasserstein distances
7. Displacement interpolation
8. The Monge—Mather shortening principle
9. Solution of the Monge problem I: global approach
10. Solution of the Monge problem II: Local approach
11. The Jacobian equation
12. Smoothness
13. Qualitative picture
II. Optimal transport and Riemannian geometry
14. Ricci curvature
15. Otto calculus
16. Displacement convexity I
17. Displacement convexity II
18. Volume control
19. Density control and local regularity
20. Infinitesimal displacement convexity
21. Isoperimetric-type inequalities
22. Concentration inequalities
23. Gradient flows I
24. Gradient flows II: Qualitative properties
25. Gradient flows III: Functional inequalities
III. Synthetic treatment of Ricci curvature
26. Analytic and synthetic points of view
27. Convergence of metric-measure spaces
28. Stability of optimal transport
29. Weak Ricci curvature bounds I: Definition and Stability
30. Weak Ricci curvature bounds II: Geometric and analytic properties
Nyckelord: MATHEMATICS / General MAT000000
- Författare
- Villani, Cédric
- Utgivare
- Springer
- Utgivningsår
- 2009
- Språk
- en
- Utgåva
- 1
- Kategori
- Naturvetenskaper
- Format
- E-bok
- eISBN (PDF)
- 9783540710509