The Resource Optimal Transport : Old and New, by Cédric Villani, (electronic resource)

Optimal Transport : Old and New, by Cédric Villani, (electronic resource)

Label
Optimal Transport : Old and New
Title
Optimal Transport
Title remainder
Old and New
Statement of responsibility
by Cédric Villani
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
Member of
Is Subseries of
http://library.link/vocab/creatorName
Villani, Cédric
Dewey number
519.6
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
m6JNIPPIcmM
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,
Series volume
338
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Mathematical optimization
  • Global differential geometry
  • Partial Differential Equations
  • Calculus of Variations and Optimal Control; Optimization
  • Differential Geometry
Label
Optimal Transport : Old and New, by Cédric Villani, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Couplings and changes of variables -- Three examples of coupling techniques -- The founding fathers of optimal transport -- Qualitative description of optimal transport -- Basic properties -- Cyclical monotonicity and Kantorovich duality -- The Wasserstein distances -- Displacement interpolation -- The Monge—Mather shortening principle -- Solution of the Monge problem I: global approach -- Solution of the Monge problem II: Local approach -- The Jacobian equation -- Smoothness -- Qualitative picture -- Optimal transport and Riemannian geometry -- Ricci curvature -- Otto calculus -- Displacement convexity I -- Displacement convexity II -- Volume control -- Density control and local regularity -- Infinitesimal displacement convexity -- Isoperimetric-type inequalities -- Concentration inequalities -- Gradient flows I -- Gradient flows II: Qualitative properties -- Gradient flows III: Functional inequalities -- Synthetic treatment of Ricci curvature -- Analytic and synthetic points of view -- Convergence of metric-measure spaces -- Stability of optimal transport -- Weak Ricci curvature bounds I: Definition and Stability -- Weak Ricci curvature bounds II: Geometric and analytic properties
Dimensions
unknown
Edition
1st ed. 2009.
Extent
1 online resource (969 p.)
Form of item
online
Isbn
9781281851208
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-540-71050-9
Specific material designation
remote
System control number
  • (CKB)1000000000546315
  • (EBL)417196
  • (OCoLC)310352213
  • (SSID)ssj0000215751
  • (PQKBManifestationID)11169067
  • (PQKBTitleCode)TC0000215751
  • (PQKBWorkID)10184954
  • (PQKB)10489119
  • (DE-He213)978-3-540-71050-9
  • (MiAaPQ)EBC417196
  • (EXLCZ)991000000000546315
Label
Optimal Transport : Old and New, by Cédric Villani, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Couplings and changes of variables -- Three examples of coupling techniques -- The founding fathers of optimal transport -- Qualitative description of optimal transport -- Basic properties -- Cyclical monotonicity and Kantorovich duality -- The Wasserstein distances -- Displacement interpolation -- The Monge—Mather shortening principle -- Solution of the Monge problem I: global approach -- Solution of the Monge problem II: Local approach -- The Jacobian equation -- Smoothness -- Qualitative picture -- Optimal transport and Riemannian geometry -- Ricci curvature -- Otto calculus -- Displacement convexity I -- Displacement convexity II -- Volume control -- Density control and local regularity -- Infinitesimal displacement convexity -- Isoperimetric-type inequalities -- Concentration inequalities -- Gradient flows I -- Gradient flows II: Qualitative properties -- Gradient flows III: Functional inequalities -- Synthetic treatment of Ricci curvature -- Analytic and synthetic points of view -- Convergence of metric-measure spaces -- Stability of optimal transport -- Weak Ricci curvature bounds I: Definition and Stability -- Weak Ricci curvature bounds II: Geometric and analytic properties
Dimensions
unknown
Edition
1st ed. 2009.
Extent
1 online resource (969 p.)
Form of item
online
Isbn
9781281851208
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-540-71050-9
Specific material designation
remote
System control number
  • (CKB)1000000000546315
  • (EBL)417196
  • (OCoLC)310352213
  • (SSID)ssj0000215751
  • (PQKBManifestationID)11169067
  • (PQKBTitleCode)TC0000215751
  • (PQKBWorkID)10184954
  • (PQKB)10489119
  • (DE-He213)978-3-540-71050-9
  • (MiAaPQ)EBC417196
  • (EXLCZ)991000000000546315

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