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A Comprehensive Introduction to Sub-Riemannian Geometry

2019-10-31 Mathematics
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Release : 2019-10-31
Genre : Mathematics
Kind : eBook
Book Rating : 35X/5 ( reviews)

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Book Synopsis A Comprehensive Introduction to Sub-Riemannian Geometry by : Andrei Agrachev

Download or read book A Comprehensive Introduction to Sub-Riemannian Geometry written by Andrei Agrachev. This book was released on 2019-10-31. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.

Sub-Riemannian Geometry

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 101/5 ( reviews)

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Book Synopsis Sub-Riemannian Geometry by : Andre Bellaiche

Download or read book Sub-Riemannian Geometry written by Andre Bellaiche. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: control theory classical mechanics Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) diffusion on manifolds analysis of hypoelliptic operators Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: Andr Bellache: The tangent space in sub-Riemannian geometry Mikhael Gromov: Carnot-Carathodory spaces seen from within Richard Montgomery: Survey of singular geodesics Hctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers Jean-Michel Coron: Stabilization of controllable systems.

Sub-Riemannian Geometry and Optimal Transport

2014-04-03 Mathematics
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Release : 2014-04-03
Genre : Mathematics
Kind : eBook
Book Rating : 04X/5 ( reviews)

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Book Synopsis Sub-Riemannian Geometry and Optimal Transport by : Ludovic Rifford

Download or read book Sub-Riemannian Geometry and Optimal Transport written by Ludovic Rifford. This book was released on 2014-04-03. 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.

A Comprehensive Introduction to Sub-Riemannian Geometry

2019-10-31 Mathematics
Download A Comprehensive Introduction to Sub-Riemannian Geometry PDF Online Free

Author :
Release : 2019-10-31
Genre : Mathematics
Kind : eBook
Book Rating : 251/5 ( reviews)

GET EBOOK


Book Synopsis A Comprehensive Introduction to Sub-Riemannian Geometry by : Andrei Agrachev

Download or read book A Comprehensive Introduction to Sub-Riemannian Geometry written by Andrei Agrachev. This book was released on 2019-10-31. Available in PDF, EPUB and Kindle. Book excerpt: Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.

An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem

2007-08-08 Mathematics
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Release : 2007-08-08
Genre : Mathematics
Kind : eBook
Book Rating : 337/5 ( reviews)

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Book Synopsis An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem by : Luca Capogna

Download or read book An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem written by Luca Capogna. This book was released on 2007-08-08. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an up-to-date account of progress on Pansu's celebrated problem on the sub-Riemannian isoperimetric profile of the Heisenberg group. It also serves as an introduction to the general field of sub-Riemannian geometric analysis. It develops the methods and tools of sub-Riemannian differential geometry, nonsmooth analysis, and geometric measure theory suitable for attacks on Pansu's problem.

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