Sub-Riemannian Geometry and Optimal Transport

Download or read book Sub-Riemannian Geometry and Optimal Transport written by Ludovic Rifford and published by Springer Science & Business Media. This book was released on 2014-04-03 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.