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书名 最优输运(第2分册)(英文版)
分类 科学技术-自然科学-物理
作者 (法)维拉尼
出版社 世界图书出版公司
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维拉尼编著的《最优输运(第2分册)(英文版)》原版980页,是单卷本,为了便于读者阅读,影印版分为2卷。全面讲述最优输运——无论新老问题的专著。本书讲学严谨,基于大量的文献扩充改变而成,使得这本书成为一本相当有价值的宝典类书籍,证明完整自成体系,扩充了文献注解。适于最优输运方面的每个科研人员和研究生,博士及以上的人员不需要预备知识可以完全读懂该书。

目录

Preface

Conventions

Introduction

 1 Couplings and changes of variables

 2 Three examples of coupling techniques

 3 The founding fathers of optimal transport

Part I Qualitative description of optimal transport

 4 Basic properties

 5 Cyclical monotonicity and Kantorovich duality

 6 The Wasserstein distances

 7 Displacement interpolation

 8 The Monge-Mather shortening principle

 9 Solution of the Monge problem I: Global approach

 10 Solution of the Monge problem II: Local approach

 11 The Jacobian equation

 12 Smoothness

 13 Qualitative picture

Part II Optimal transport and Riemannian geometry

 14 Ricci curvature

 15 Otto calculus

 16 Displacement convexity I

 17 Displacement convexity II

 18 Volume control

 19 Density control and local regularity

 20 Infinitesimal displacement convexity

 21 Isoperimetric-type inequalities

 22 Concentration inequalities

 23 Gradient flows I

 24 Gradient flows II: Qualitative properties

 25 Gradient flows III: Functional inequalities

Part III Synthetic treatment of Ricci curvature

 26 Analytic and synthetic points of view

 27 Convergence of metric-measure spaces

 28 Stability of optimal transport

 29 Weak Ricci curvature bounds I" Definition

 and Stability

 30 Weak Ricci curvature bounds II: Geometric

 and analytic properties

Conclusions and open problems

 References

 List of short statements

 List of figures

 Index

 Some notable cost functions

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