Optimal Transport

Old and New

Authors:

ISBN: 978-3-540-71049-3 (Print) 978-3-540-71050-9 (Online)

Table of contents (30 chapters)

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  1. Front Matter

    Pages I-XXII

  2. Introduction

    1. Front Matter

      Pages 1-3

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      Book Chapter

      Pages 5-20

      Couplings and changes of variables

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      Book Chapter

      Pages 21-28

      Three examples of coupling techniques

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      Book Chapter

      Pages 29-37

      The founding fathers of optimal transport

  3. Qualitative description of optimal transport

    1. Front Matter

      Pages 39-41

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      Book Chapter

      Pages 43-49

      Basic properties

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      Book Chapter

      Pages 51-92

      Cyclical monotonicity and Kantorovich duality

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      Book Chapter

      Pages 93-111

      The Wasserstein distances

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      Book Chapter

      Pages 113-162

      Displacement interpolation

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      Book Chapter

      Pages 163-203

      The Monge—Mather shortening principle

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      Book Chapter

      Pages 205-213

      Solution of the Monge problem I: global approach

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      Book Chapter

      Pages 215-272

      Solution of the Monge problem II: Local approach

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      Book Chapter

      Pages 273-279

      The Jacobian equation

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      Book Chapter

      Pages 281-332

      Smoothness

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      Book Chapter

      Pages 333-351

      Qualitative picture

  4. Optimal transport and Riemannian geometry

    1. Front Matter

      Pages 353-356

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      Book Chapter

      Pages 357-420

      Ricci curvature

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      Book Chapter

      Pages 421-433

      Otto calculus

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      Book Chapter

      Pages 435-447

      Displacement convexity I

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      Book Chapter

      Pages 449-492

      Displacement convexity II

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      Book Chapter

      Pages 493-504

      Volume control

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      Book Chapter

      Pages 505-524

      Density control and local regularity

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      Book Chapter

      Pages 525-543

      Infinitesimal displacement convexity

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