Sub-Riemannian Geometry and Optimal Transport - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sub-Riemannian Geometry and Optimal Transport write by Ludovic Rifford. This book was released on 2014-04-03. Sub-Riemannian Geometry and Optimal Transport available in PDF, EPUB and Kindle. 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.
A Comprehensive Introduction to Sub-Riemannian Geometry
A Comprehensive Introduction to Sub-Riemannian Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Comprehensive Introduction to Sub-Riemannian Geometry write by Andrei Agrachev. This book was released on 2019-10-31. A Comprehensive Introduction to Sub-Riemannian Geometry available in PDF, EPUB and Kindle. Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.
Noncommutative Geometry and Optimal Transport
Noncommutative Geometry and Optimal Transport - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Geometry and Optimal Transport write by Pierre Martinetti. This book was released on 2016-10-26. Noncommutative Geometry and Optimal Transport available in PDF, EPUB and Kindle. The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.
Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning
Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning write by Frédéric Jean. This book was released on 2014-07-17. Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning available in PDF, EPUB and Kindle. Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.
Optimal Transport
Optimal Transport - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Transport write by Cédric Villani. This book was released on 2008-10-26. Optimal Transport available in PDF, EPUB and Kindle. At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
