Strong displacement convexity on Riemannian manifolds

Mathematische Zeitschrift

Volumn 257, Issue 2, 2007, Pages 251-259

  Figalli, A ^a,b   Villani, C ^a  

^a UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

^b SCUOLA NORMALE SUPERIORE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547435369     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-007-0124-5     Document Type: Article

References (10)

1. Cordero-Erausquin D., McCann R.J. and Schmuckenschläger M. (2001). A Riemannian interpolation inequality à la Borell, Brascamp and Lieb. Invent. Math. 146(2): 219-257
2. Fathi, A., Figalli, A.: Optimal transportation on non-compact manifolds. Preprint (2006)
3. Figalli, A.: Existence, uniqueness and regularity of optimal transport maps. SIAM J. Math. Anal. (to appear). Available online via http://cvgmt.sns.it/ people/figalli/
4. Lott, J., Villani, C.: Ricci curvature for metric-measure spaces via optimal transport. Ann. of Math. (to appear). Available online via http://www.umpa.ens-lyon.fr/cvillani/
5. Otto F. and Villani C. (2000). Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173(2): 361-400
6. Sturm K.-T. (2006). On the geometry of metric measure spaces. I. Acta Math. 196(1): 65-131
7. Sturm K.-T. (2006). On the geometry of metric measure spaces. II. Acta Math. 196(1): 133-177
8. Sturm K.-T. and Renesse M.-K. (2005). Transport inequalities, gradient estimates, entropy and Ricci curvature. Commun. Pure Appl. Math. 58(7): 923-940
9. Villani, C.: Topics in optimal transportation. Graduate Studies in Mathematics, vol. 58. American Mathematical Society, Providence, RI (2003)
10. Villani, C.: Optimal transport, old and new. Notes from the Saint-Flour 2005 Summer School. Available online at http://www.umpa.ens-lyon.fr/ cvillani/