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008			080630s2009 gw a b 001 0 eng d
010			_a 2008932183
020			_a9783540710493 (acidfree paper)
020			_a3540710493 (acidfree paper)
020			_a9783540710509 (e-ISBN)
040			_aEC-UrYT _cEC-UrYT _dEC-UrYT
041			_aeng
042			_alccopycat
082	0	4	_a519.6 _223
100	1		_aVillani, Cédric _d1973- _97409
245	1	0	_aOptimal transport : _bold and new / _cCédric Villani.
250			_aFirst Edition.
264	3	4	_aBerlin : _bSpringer ; _c2009.
300			_axxii, 973 pages : _billustrations ; _c24 cm.
490	0		_aGrundlehren der mathematischen Wissenschaften, _x0072-7830 ; _v338.
504			_aIncludes bibliographical references (pages 915-956) and index.
505	2		_a1 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 inequalties -- 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.
520	3		_aAt 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.
650	2	4	_aMathematical optimization _92345
650	2	4	_aTransportation problems (Programming) _97411
650	2	4	_aProbabilities _9532
650	2	4	_aDynamics. _95768
650	2	4	_aOptimización matemática _9281
650	2	4	_aProblemas de transporte (Programación) _97487
650	2	4	_aProbabilidades _91339
650	2	4	_aDinámica _9405
830		0	_aGrundlehren der mathematischen Wissenschaften ; _v338.
856	4		_mDE-576;springer _qimage/jpeg _uhttp://swbplus.bsz-bw.de/bsz28657621xcov.htm _v20090331045625 _3Cover
856	4		_mDE-576;springer _qapplication/pdf _uhttp://swbplus.bsz-bw.de/bsz28657621xkap.htm _v20081111120118 _3Kapitel 1
856	4		_mDE-576;springer _qapplication/pdf _uhttp://swbplus.bsz-bw.de/bsz28657621xvor.htm _v20081111120129 _3Vorwort 1
856	4		_mDE-576;springer _qapplication/pdf _uhttp://swbplus.bsz-bw.de/bsz28657621xinh.htm _v20081111120135 _3Inhaltsverzeichnis
856	4		_uhttp://digitool.hbz-nrw.de:1801/webclient/DeliveryManager?pid=2645708&custom%5Fatt%5F2=simple%5Fviewer _xVerlag
906			_a7 _bcbc _ccopycat _d2 _encip _f20 _gy-gencatlg
942			_2ddc _cLIBRO
955			_bxh14 2012-06-05 z-processor _ath83 2012-06-05 to USPL/STM _arf09 2012-06-25 add'l. copy rec'd. _ixh58 2012-07-23 ; to BCCD
955			_apc17 2008-06-30