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Optimal transport : old and new

Autor: Cédric Villani
Editora: Berlin : Springer, cop. 2009.
Séries: Grundlehren der mathematischen Wissenschaften, 338.
Edição/Formato   Print book : InglêsVer todas as edições e formatos
Base de Dados:WorldCat
Resumo:

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  Ler mais...

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Detalhes

Tipo de Documento: Livro
Todos os Autores / Contribuintes: Cédric Villani
ISBN: 9783540710493 3540710493
Número OCLC: 494664787
Notas: Contient des exercices
Descrição: 1 vol. (XXII-973 p.) : fig. ; 24 cm.
Conteúdos: 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.
Título da Série: Grundlehren der mathematischen Wissenschaften, 338.
Outros Títulos: Contient des exercices.
Responsabilidade: 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 Ler mais...

 
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