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  • Séminaire de théorie spectrale et géométrie
  • Volume 25 (2006-2007)
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Transport de mesures sur un espace d’Alexandrov
Jérôme Bertrand1
1 Université de Toulouse Institut de Mathématiques UMR 5219 (UPS-CNRS) 118, route de Narbonne 31062 Cedex 4 Toulouse (France)
Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 17-24.
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MR   Zbl
DOI: 10.5802/tsg.244
Author's affiliations:
Jérôme Bertrand 1

1 Université de Toulouse Institut de Mathématiques UMR 5219 (UPS-CNRS) 118, route de Narbonne 31062 Cedex 4 Toulouse (France)
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@article{TSG_2006-2007__25__17_0,
     author = {J\'er\^ome Bertrand},
     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},
     mrnumber = {2478805},
     zbl = {1163.49043},
     language = {fr},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.244/}
}
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AU  - Jérôme Bertrand
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  - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.244/
DO  - 10.5802/tsg.244
LA  - fr
ID  - TSG_2006-2007__25__17_0
ER  - 
%0 Journal Article
%A Jérôme Bertrand
%T Transport de mesures sur un espace d’Alexandrov
%J Séminaire de théorie spectrale et géométrie
%D 2006-2007
%P 17-24
%V 25
%I Institut Fourier
%C Grenoble
%U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.244/
%R 10.5802/tsg.244
%G fr
%F TSG_2006-2007__25__17_0
Jérôme Bertrand. Transport de mesures sur un espace d’Alexandrov. Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 17-24. doi : 10.5802/tsg.244. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.244/
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[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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