Lectures on Optimal Transport
This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transpor...
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| Main Authors: | , , |
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| Institution som forfatter: | |
| Format: | Electronisk eBog |
| Sprog: | engelsk |
| Udgivet: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Udgivelse: | 2nd ed. 2024. |
| Serier: | La Matematica per il 3+2,
169 |
| Fag: | |
| Online adgang: | https://doi.org/10.1007/978-3-031-76834-7 |
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Indholdsfortegnelse:
- - 1. Lecture I. Preliminary notions and the Monge problem
- 2. Lecture II. The Kantorovich problem
- 3. Lecture III. The Kantorovich - Rubinstein duality
- 4. Lecture IV. Necessary and sufficient optimality conditions
- 5. Lecture V. Existence of optimal maps and applications
- 6. Lecture VI. A proof of the isoperimetric inequality and stability in Optimal Transport
- 7. Lecture VII. The Monge-Ampére equation and Optimal Transport on Riemannian manifolds
- 8. Lecture VIII. The metric side of Optimal Transport
- 9. Lecture IX. Analysis on metric spaces and the dynamic formulation of Optimal Transport
- 10. Lecture X.Wasserstein geodesics, nonbranching and curvature
- 11. Lecture XI. Gradient flows: an introduction
- 12. Lecture XII. Gradient flows: the Brézis-Komura theorem
- 13. Lecture XIII. Examples of gradient flows in PDEs
- 14. Lecture XIV. Gradient flows: the EDE and EDI formulations
- 15. Lecture XV. Semicontinuity and convexity of energies in the Wasserstein space
- 16. Lecture XVI. The Continuity Equation and the Hopf-Lax semigroup
- 17. Lecture XVII. The Benamou-Brenier formula
- 18. Lecture XVIII. An introduction to Otto’s calculus
- 19. Lecture XIX. Heat flow, Optimal Transport and Ricci curvature.