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Sub-Riemannian Geometry and Optimal Transport

  • Book
  • © 2014

Overview

Authors:
  1. Ludovic Rifford

    1. Laboratoire J.A. Dieudonné, Université Nice Sophia Antipolis, Nice, France

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  • Crash course in both sub-Riemannian geometry and optimal transport
  • Recent results and state-of-the-art on optimal transport in sub-Riemannian geometry
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-vii
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  2. Sub-Riemannian Structures

    • Ludovic Rifford
    Pages 1-36

  3. Sub-Riemannian Geodesics

    • Ludovic Rifford
    Pages 37-76

  4. Introduction to Optimal Transport

    • Ludovic Rifford
    Pages 77-119

  5. Back Matter

    Pages 121-140
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Keywords

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.

Authors and Affiliations

  • Laboratoire J.A. Dieudonné, Université Nice Sophia Antipolis, Nice, France

    Ludovic Rifford

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