Sub-Riemannian Geometry and Optimal Transport

  • Ludovic Rifford

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Ludovic Rifford
    Pages 1-36
  3. Ludovic Rifford
    Pages 37-76
  4. Ludovic Rifford
    Pages 77-119
  5. Back Matter
    Pages 121-140

About this book


The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.


analysis optimal control optimal transport singular controls sub-Riemannian geometry

Authors and affiliations

  • Ludovic Rifford
    • 1
  1. 1.Laboratoire J.A. DieudonnéUniversité Nice Sophia AntipolisNiceFrance

Bibliographic information

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