維拉尼所著《*輸運（第1分冊）（英文版）》是全面講述*輸運——無論新老問題的專著。本書講學(xué)嚴(yán)謹(jǐn)，基于大量的文獻(xiàn)擴(kuò)充改變而成，使得這本書成為一本相當(dāng)有價值的寶典類書籍，證明完整自成體系，擴(kuò)充了文獻(xiàn)注解。適于*輸運方面的每個科研人員和研究生，博士及以上的人員不需要預(yù)備知識可以完全讀懂該書。
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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