Synthetic theory of Ricci curvature bounds

Abstract

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

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Correspondence to Cédric Villani.

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This article is based on the 15th Takagi Lectures that the author delivered at Tohoku University on June 27 and 28, 2015.

Communicated by: Toshiyuki Kobayashi

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Villani, C. Synthetic theory of Ricci curvature bounds. Jpn. J. Math. 11, 219–263 (2016). https://doi.org/10.1007/s11537-016-1531-3

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Keywords and phrases

  • Ricci curvature
  • optimal transport
  • metric geometry
  • synthetic geometry
  • information geometry

Mathematics Subject Classification (2010)

  • 53B21
  • 90C08