Transport de mesures sur un espace d’Alexandrov

Jérôme Bertrand[1]

  • [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 (2006-2007)

  • Volume: 25, page 17-24
  • ISSN: 1624-5458

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Bertrand, Jérôme. "Transport de mesures sur un espace d’Alexandrov." Séminaire de théorie spectrale et géométrie 25 (2006-2007): 17-24. <http://eudml.org/doc/11224>.

@article{Bertrand2006-2007,
affiliation = {Université de Toulouse Institut de Mathématiques UMR 5219 (UPS-CNRS) 118, route de Narbonne 31062 Cedex 4 Toulouse (France)},
author = {Bertrand, Jérôme},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {optimal transport; Alexandrov space; Ricci minor},
language = {fre},
pages = {17-24},
publisher = {Institut Fourier},
title = {Transport de mesures sur un espace d’Alexandrov},
url = {http://eudml.org/doc/11224},
volume = {25},
year = {2006-2007},
}

TY - JOUR
AU - Bertrand, Jérôme
TI - Transport de mesures sur un espace d’Alexandrov
JO - Séminaire de théorie spectrale et géométrie
PY - 2006-2007
PB - Institut Fourier
VL - 25
SP - 17
EP - 24
LA - fre
KW - optimal transport; Alexandrov space; Ricci minor
UR - http://eudml.org/doc/11224
ER -

References

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  2. Jérôme Bertrand. Existence and uniqueness of optimal maps on Alexandrov spaces. Preprint 2007. Zbl1149.49002
  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. Zbl0802.53018MR1185284
  4. John Lott and Cédric Villani. Ricci curvature for metric-measure spaces via optimal mass transport. To appear in Annals of math. Zbl1178.53038
  5. John Lott and Cédric Villani. Weak curvature conditions and poincaré inequalities. J. Funct. Anal. 245(1) : 311–333, 2007. Zbl1119.53028MR2311627
  6. John Lott. Optimal transport and Ricci curvature for metric-measure spaces. Surveys in Differential Geometry XI (2007). Zbl1155.53026
  7. Robert J. McCann. Polar factorization of maps on Riemannian manifolds. Geom. Funct. Anal., 11(3) :589–608, 2001. Zbl1011.58009MR1844080
  8. Yukio Otsu and Takashi Shioya. The Riemannian structure of Alexandrov spaces. J. Differential Geom., 39(3) :629–658, 1994. Zbl0808.53061MR1274133
  9. Karl-Theodor Sturm. On the geometry of metric measure spaces. I. Acta Math., 196(1) :65–131, 2006. Zbl1105.53035MR2237206
  10. Karl-Theodor Sturm. On the geometry of metric measure spaces. II. Acta Math., 196(1) :133–177, 2006. Zbl1106.53032MR2237207
  11. Cédric Villani. Topics in optimal transportation., volume 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2003. Zbl1106.90001MR1964483
  12. Cédric Villani. Optimal transport, old and new (to appear). Zbl1156.53003
  13. Guofang Wei. Manifolds with A Lower Ricci Curvature Bound. Surveys in Differential Geometry XI (2007). Zbl1151.53036
  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. Zbl0896.53036MR1452876

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