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Overview"This is the first comprehensive introduction to the theory of mass transportation with its many-and sometimes unexpected-applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. In 1781, Gaspard Monge defined the problem of ""optimal transportation"" (or the transferring of mass with the least possible amount of work), with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis." Full Product DetailsAuthor: Cédric VillaniPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 58 Dimensions: Width: 18.30cm , Height: 2.50cm , Length: 23.00cm Weight: 0.840kg ISBN: 9780821833124ISBN 10: 082183312 Pages: 370 Publication Date: 30 March 2003 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsPreface Notation Introduction The Kantorovich duality Geometry of optimal transportation Brenier’s polar factorization theorem The Monge-Ampère equation Displacement interpolation and displacement convexity Geometric and Gaussian inequalities The metric side of optimal transportation A differential point of view on optimal transportation Entropy production and transportation inequalities Problems Bibliography Table of short statements IndexReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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