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...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2009.
|
| Σειρά: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
338 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.
