Sub-Riemannian Geometry and Optimal Transport

✍ Scribed by Ludovic Rifford (auth.)

Publisher: Springer International Publishing
Year: 2014
Tongue: English
Leaves: 146
Series: SpringerBriefs in Mathematics
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-vii
Sub-Riemannian Structures....Pages 1-36
Sub-Riemannian Geodesics....Pages 37-76
Introduction to Optimal Transport....Pages 77-119
Back Matter....Pages 121-140

✦ Subjects

Analysis; Differential Geometry; Optimization; Measure and Integration; Systems Theory, Control

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