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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2009.
|
| Edición: | 1st ed. 2009. |
| Colección: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
338 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-540-71050-9 | ||
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| 020 | |a 9783540710509 |9 978-3-540-71050-9 | ||
| 024 | 7 | |a 10.1007/978-3-540-71050-9 |2 doi | |
| 050 | 4 | |a QA370-380 | |
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| 100 | 1 | |a Villani, Cédric. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Optimal Transport |h [electronic resource] : |b Old and New / |c by Cédric Villani. |
| 250 | |a 1st ed. 2009. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2009. | |
| 300 | |a XXII, 976 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |x 2196-9701 ; |v 338 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book's value as a most welcome reference text on this subject. . | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Calculus of variations. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 1 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Calculus of Variations and Optimization. |
| 650 | 2 | 4 | |a Differential Geometry. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783540867456 |
| 776 | 0 | 8 | |i Printed edition: |z 9783540710493 |
| 776 | 0 | 8 | |i Printed edition: |z 9783662501801 |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |x 2196-9701 ; |v 338 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-540-71050-9 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||