Japanese Journal of Mathematics

, Volume 11, Issue 2, pp 219–263

Synthetic theory of Ricci curvature bounds

Takagi Lectures

DOI: 10.1007/s11537-016-1531-3

Cite this article as:
Villani, C. Jpn. J. Math. (2016) 11: 219. doi:10.1007/s11537-016-1531-3


Synthetic theory of Ricci curvature bounds is reviewed, from the conditions which led to its birth, up to some of its latest developments.

Keywords and phrases

Ricci curvature optimal transport metric geometry synthetic geometry information geometry 

Mathematics Subject Classification (2010)

53B21 90C08 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2016

Authors and Affiliations

  1. 1.Université de Lyon Claude Bernard & French Academy of Sciences and Institut Henri PoincaréParis Cedex 05France

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