Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds

Comptes Rendus Mathematique

Volumn 345, Issue 3, 2007, Pages 151-154

  Savaré, Giuseppe ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34547422503     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.06.018     Document Type: Article

References (11)

1. Ambrosio L., Gigli N., and Savaré G. Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Zürich (2005), Birkhäuser Verlag, Basel
2. Ambrosio L., and Savaré G. Gradient flows of probability measures. Handbook of Evolution Equations (III) (2006), Elsevier
3. Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Mathematics Studies, No. 5 (1973), North-Holland Publishing Co., Amsterdam
4. Burago D., Burago Y., and Ivanov S. A Course in Metric Geometry. Graduate Studies in Mathematics vol. 33 (2001), American Mathematical Society, Providence, RI
5. Jordan R., Kinderlehrer D., and Otto F. The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1-17
6. J. Lott, C. Villani, Ricci curvature for metric-measure spaces via optimal transport, Ann. Math., in press
7. Mayer U.F. Gradient flows on nonpositively curved metric spaces and harmonic maps. Comm. Anal. Geom. 6 (1998) 199-253
8. S.-I. Ohta, Gradient flows on Wasserstein spaces over compact Alexandrov spaces, preprint, 2007
9. G. Perelman, A. Petrunin, Quasigeodesics and gradient curves in Alexandrov spaces, unpublished manuscript
10. Sturm K.-T. On the geometry of metric measure spaces. I. Acta Math. 196 (2006) 65-131
11. Villani C. Topics in Optimal Transportation. Graduate Studies in Mathematics vol. 58 (2003), American Mathematical Society, Providence, RI