作者：维拉尼
页数：729
出版社：世界图书出版公司
出版日期：2014
ISBN：9787510077906
电子书格式：pdf/epub/txt
内容简介
本书原版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。
作者简介
Cédric Villani是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
本书特色
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
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
