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Villani, Cédric

Optimal Transport

Villani, Cédric - Optimal Transport, ebook

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ISBN: 9783540710509
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Table of contents

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

Keywords: MATHEMATICS / General MAT000000

Author(s)
Publisher
Springer
Publication year
2009
Language
en
Edition
1
Category
Natural Sciences
Format
Ebook
eISBN (PDF)
9783540710509

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