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美国数学会经典影印系列 最优输运理论专题 第2版PDF|Epub|txt|kindle电子书版本网盘下载
- 塞德里克维拉尼著 著
- 出版社： 北京：高等教育出版社
- ISBN：9787040469214
- 出版时间：2017
- 标注页数：381页
- 文件大小：149MB
- 文件页数：399页
- 主题词：
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图书目录
Introduction1
1．Formulation of the optimal transportation problem1
2．Basic questions6
3．Overview of the course10
Chapter 1．The Kantorovich Duality17
1.1．General duality17
1.2．Distance cost functions34
1.3．Appendix:A duality argument in Cb（X×Y）39
1.4．Appendix:｛0,1｝-valued costs and Strassen's theorem44
Chapter 2． Geometry of Optimal Transportation49
2.1．A duality-based proof for the quadratic cost50
2.2．The real line75
2.3．Alternative arguments80
2.4．Generalizations to other costs87
2.5．More on c-concave functions105
Chapter 3．Brenier's Polar Factorization Theorem109
3.1．Rearrangements and polar factorization109
3.2．Historical motivations:fluid mechanics113
3.3．Proof of Brenier's polar factorization theorem121
3.4．Related facts124
Chapter 4．The Monge-Ampère Equation127
4.1．Informal presentation127
4.2．Regularity133
4.3．Open problems143
Chapter 5．Displacement Interpolation and Displacement Convexity145
5.1．Displacement interpolation145
5.2．Displacement convexity152
5.3．Application:uniqueness of ground state166
5.4．The Eulerian point of view168
Chapter 6．Geometric and Gaussian Inequalities187
6.1．Brunn-Minkowski and Prékopa-Leindler inequalities188
6.2．The Alesker-Dar-Milman diffeomorphism194
6.3．Gaussian inequalities197
6.4．Sobolev inequalities204
Chapter 7．The Metric Side of Optimal Transportation209
7.1．Monge-Kantorovich distances211
7.2．Topological properties216
7.3．The real line222
7.4．Behavior under rescaled convolution224
7.5．An application to the Boltzmann equation227
7.6．Linearization237
Chapter 8．A Differential Point of View on Optimal Transportation241
8.1．A differential formulation of optimal transportation242
8.2．Differential calculus in（P（Rn），W2）254
8.3．Monge-Kantorovich induced dynamics255
8.4．Time-discretization260
8.5．Differentiability of the quadratic Wasserstein distance266
8.6．Non-quadratic costs270
Chapter 9．Entropy Production and Transportation Inequalities271
9.1．More on optimal-transportation induced dissipative equations272
9.2．Logarithmic Sobolev inequalities283
9.3．Talagrand inequalities295
9.4．HWI inequalities301
9.5．Nonlinear generalizations:internal energy305
9.6．Nonlinear generalizations:interaction energy308
Chapter 10．Problems311
List of Problems312
Bibliography353
Table of Short Statements369
Index375