图文详情
- ISBN:9787510077906
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:16开
- 页数:729
- 出版时间:2014-07-01
- 条形码:9787510077906 ; 978-7-5100-7790-6
本书特色
维拉尼所著《*优输运(第1分册)(英文版)》是全面讲述*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*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。
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*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*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
展开全部
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。
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