@article{TSG_2006-2007__25__17_0, author = {Bertrand, J\'er\^ome}, title = {Transport de mesures sur un espace {d{\textquoteright}Alexandrov}}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {17--24}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {25}, year = {2006-2007}, doi = {10.5802/tsg.244}, zbl = {1163.49043}, mrnumber = {2478805}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/tsg.244/} }
TY - JOUR AU - Bertrand, Jérôme TI - Transport de mesures sur un espace d’Alexandrov JO - Séminaire de théorie spectrale et géométrie PY - 2006-2007 SP - 17 EP - 24 VL - 25 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/tsg.244/ DO - 10.5802/tsg.244 LA - fr ID - TSG_2006-2007__25__17_0 ER -
Bertrand, Jérôme. Transport de mesures sur un espace d’Alexandrov. Séminaire de théorie spectrale et géométrie, Tome 25 (2006-2007), pp. 17-24. doi : 10.5802/tsg.244. http://www.numdam.org/articles/10.5802/tsg.244/
[1] Dominique Bakry and Michel Émery. Diffusions hypercontractives. In Séminaire de probabilités, XIX, 1983/84, volume 1123 of Lecture Notes in Math., pages 177–206. Springer, Berlin, 1985. | Numdam | MR | Zbl
[2] Jérôme Bertrand. Existence and uniqueness of optimal maps on Alexandrov spaces. Preprint 2007.
[3] Yuri Burago, Mikhail Gromov, and Gregory Perelman. A. D. Aleksandrov spaces with curvatures bounded below. Uspekhi Mat. Nauk, 47(2(284)) :3–51, 222, 1992. | MR | Zbl
[4] John Lott and Cédric Villani. Ricci curvature for metric-measure spaces via optimal mass transport. To appear in Annals of math.
[5] John Lott and Cédric Villani. Weak curvature conditions and poincaré inequalities. J. Funct. Anal. 245(1) : 311–333, 2007. | MR | Zbl
[6] John Lott. Optimal transport and Ricci curvature for metric-measure spaces. Surveys in Differential Geometry XI (2007).
[7] Robert J. McCann. Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal., 11(3) :589–608, 2001. | MR | Zbl
[8] Yukio Otsu and Takashi Shioya. The Riemannian structure of Alexandrov spaces. J. Differential Geom., 39(3) :629–658, 1994. | MR | Zbl
[9] Karl-Theodor Sturm. On the geometry of metric measure spaces. I. Acta Math., 196(1) :65–131, 2006. | MR | Zbl
[10] Karl-Theodor Sturm. On the geometry of metric measure spaces. II. Acta Math., 196(1) :133–177, 2006. | MR | Zbl
[11] Cédric Villani. Topics in optimal transportation., volume 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2003. | MR | Zbl
[12] Cédric Villani. Optimal transport, old and new (to appear).
[13] Guofang Wei. Manifolds with A Lower Ricci Curvature Bound. Surveys in Differential Geometry XI (2007).
[14] Shunhui Zhu. The comparison geometry of Ricci curvature. In Comparison geometry (Berkeley, CA, 1993–94), volume 30 of Math. Sci. Res. Inst. Publ., pages 221–262. Cambridge Univ. Press, Cambridge, 1997. | MR | Zbl
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