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A User’s Guide to Optimal Transport

  • Luigi Ambrosio
  • Nicola Gigli
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2062)

Abstract

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below.

Notes

Acknowledgements

Work partially supported by a MIUR PRIN2008 grant.

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Université de Nice, MathématiquesNiceFrance

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