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Optimal transport, old and new. Notes from the Saint-Flour 2005 Summer School
C. Villani (2008)
Optimal Transport: Old and New
Karl-Theodor Sturm (2006)
On the geometry of metric measure spaces. IIActa Mathematica, 196
Max‐K. Renesse, Karl-Theodor Sturm (2005)
Transport inequalities, gradient estimates, entropy and Ricci curvatureCommunications on Pure and Applied Mathematics, 58
(2001)
A Riemannian interpolation inequalityinequalityà la Borell, Brascamp and Lieb
J. Lott, C. Villani (2004)
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A. Figalli (2007)
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F. Otto, C. Villani (2000)
Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev InequalityJournal of Functional Analysis, 173
Karl-Theodor Sturm (2006)
On the geometry of metric measure spacesActa Mathematica, 196
C. Villani (2003)
Topics in Optimal Transportation
D. Cordero-Erausquin, R. McCann, M. Schmuckenschläger (2001)
A Riemannian interpolation inequality à la Borell, Brascamp and LiebInventiones mathematicae, 146
A. Fathi, A. Figalli (2007)
Optimal transportation on non-compact manifoldsIsrael Journal of Mathematics, 175
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TOPICS IN OPTIMAL TRANSPORTATION (Graduate Studies in Mathematics 58) By CÉDRIC VILLANI: 370 pp., US$59.00, ISBN 0-8218-3312-X (American Mathematical Society, Providence, RI, 2003)Bulletin of The London Mathematical Society, 36
(2005)
Optimal transport, old and new. Notes from the Saint-Flour 2005 Summer School. Available online at www.umpa.ens-lyon.fr/~cvillani
Ricci curvature bounds in Riemannian geometry are known to be equivalent to the weak convexity (convexity along at least one geodesic between any two points) of certain functionals in the space of probability measures. We prove that the weak convexity can be reinforced into strong (usual) convexity, thus solving a question left open in Lott and Villani (Ann of Math, to appear).
Mathematische Zeitschrift – Springer Journals
Published: May 8, 2007
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