最优输运-第1分册

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