Ricci curvature and measures

  title={Ricci curvature and measures},
  author={Jean Pierre Bourguignon},
  journal={Japanese Journal of Mathematics},
  • J. Bourguignon
  • Published 28 March 2009
  • Mathematics
  • Japanese Journal of Mathematics
Abstract.In the last thirty years three a priori very different fields of mathematics, optimal transport theory, Riemannian geometry and probability theory, have come together in a remarkable way, leading to a very substantial improvement of our understanding of what may look like a very specific question, namely the analysis of spaces whose Ricci curvature admits a lower bound. The purpose of these lectures is, starting from the classical context, to present the basics of the three fields that… 

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