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Optimal Transport

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Cover of 'Optimal Transport'

Table of Contents

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    Book Overview
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    Chapter 1 Couplings and changes of variables
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    Chapter 2 Three examples of coupling techniques
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    Chapter 3 The founding fathers of optimal transport
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    Chapter 4 Basic properties
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    Chapter 5 Cyclical monotonicity and Kantorovich duality
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    Chapter 6 The Wasserstein distances
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    Chapter 7 Displacement interpolation
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    Chapter 8 The Monge—Mather shortening principle
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    Chapter 9 Solution of the Monge problem I: global approach
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    Chapter 10 Solution of the Monge problem II: Local approach
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    Chapter 11 The Jacobian equation
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    Chapter 12 Smoothness
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    Chapter 13 Qualitative picture
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    Chapter 14 Ricci curvature
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    Chapter 15 Otto calculus
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    Chapter 16 Displacement convexity I
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    Chapter 17 Displacement convexity II
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    Chapter 18 Volume control
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    Chapter 19 Density control and local regularity
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    Chapter 20 Infinitesimal displacement convexity
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    Chapter 21 Isoperimetric-type inequalities
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    Chapter 22 Concentration inequalities
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    Chapter 23 Gradient flows I
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    Chapter 24 Gradient flows II: Qualitative properties
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    Chapter 25 Gradient flows III: Functional inequalities
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    Chapter 26 Analytic and synthetic points of view
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    Chapter 27 Convergence of metric-measure spaces
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    Chapter 28 Stability of optimal transport
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    Chapter 29 Weak Ricci curvature bounds I: Definition and Stability
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    Chapter 30 Weak Ricci curvature bounds II: Geometric and analytic properties
Attention for Chapter 18: Volume control
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Chapter title
Volume control
Chapter number 18
Book title
Optimal Transport
Published by
Springer Berlin Heidelberg, January 2009
DOI 10.1007/978-3-540-71050-9_18
Book ISBNs
978-3-54-071049-3, 978-3-54-071050-9
Authors

Cédric Villani