新書推薦:

《
四海之内:中国历史四十讲
》
售價:HK$
97.9

《
万亿低空:技术核心篇 低空经济
》
售價:HK$
107.8

《
逃离邪恶(中译本首-次出版 普利策奖得主厄内斯特·贝克尔遗作 《拒斥死亡》姊妹篇)
》
售價:HK$
107.8

《
萤火虫全球史072:图说中世纪医学简史
》
售價:HK$
82.5

《
汉字中国:承载三千年中华文化的瑰宝
》
售價:HK$
42.9

《
自我救赎:战胜复杂性创伤的行动指南
》
售價:HK$
64.9

《
罗马和平新版 古代地中海世界的暴力 征服与和平 汗青堂丛书109
》
售價:HK$
116.6

《
万亿低空:应用实战篇 低空经济
》
售價:HK$
107.8
|
| 內容簡介: |
|
维拉尼所著《最优输运(第1分册)(英文版)》是全面讲述最优输运——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
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
|
|