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Optimal transport : old and new

著者: Cédric Villani
出版商: Berlin : Springer, cop. 2009.
丛书: Grundlehren der mathematischen Wissenschaften, 338.
版本/格式:   图书 : 英语查看所有的版本和格式
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The field of optimal transport has made breathtaking forays into various other domains of mathematics. This book presents a broad overview of this area. PhD students or researchers can read the  再读一些...

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所有的著者/提供者: Cédric Villani
ISBN: 9783540710493 3540710493
OCLC号码: 494664787
注意: Contient des exercices
描述: 1 vol. (XXII-973 p.) : fig. ; 24 cm.
内容: 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.
丛书名: Grundlehren der mathematischen Wissenschaften, 338.
其他题名: Contient des exercices.
责任: Cédric Villani.
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From the reviews: "The book is aimed to old and new problems of optimal transport. ... This meticulous work is based on very large bibliography ... that is converted into a very valuable monograph 再读一些...

 
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