《最優輸運·第1分冊》是2014年世界圖書出版公司出版的著作，作者是[法] 維拉尼 。
基本介紹
- 中文名：《最優輸運·第1分冊》
- 作者：[法]維拉尼
- 出版社：世界圖書出版公司
- 出版時間：2014年07月01日
- ISBN：9787510077906
內容簡介,目錄,
內容簡介
When I was first approached for the 2005 edition of the Saint-Flour Probability Summer School, I was intrigued, flattered and scared. l Apart from the challenge posed by the teaching of a rather analytical
subject to a probabilistic audience, there was the danger of producing a remake of my recent book Topics in, Optimal Transportation.
目錄
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
……
Conclusions and open problems
