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Sub Riemannian Geometry

Sub Riemannian Geometry PDF
Author: André Bellaïche
Publisher: Springer Science & Business Media
ISBN: 9783764354763
Size: 27.93 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 393
View: 4277

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Sub Riemannian Geometry

by André Bellaïche, Sub Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Sub Riemannian Geometry books, 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: • André Bellaïche: The tangent space in sub-Riemannian geometry • Mikhael Gromov: Carnot-Carathéodory spaces seen from within • Richard Montgomery: Survey of singular geodesics • Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers • Jean-Michel Coron: Stabilization of controllable systems




Geometric Control Theory And Sub Riemannian Geometry

Geometric Control Theory and Sub Riemannian Geometry PDF
Author: Gianna Stefani
Publisher: Springer
ISBN: 331902132X
Size: 29.11 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 384
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Geometric Control Theory And Sub Riemannian Geometry

by Gianna Stefani, Geometric Control Theory And Sub Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Geometric Control Theory And Sub Riemannian Geometry books, Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.




A Comprehensive Introduction To Sub Riemannian Geometry

A Comprehensive Introduction to Sub Riemannian Geometry PDF
Author: Andrei Agrachev
Publisher: Cambridge University Press
ISBN: 110847635X
Size: 78.14 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 774
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A Comprehensive Introduction To Sub Riemannian Geometry

by Andrei Agrachev, A Comprehensive Introduction To Sub Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download A Comprehensive Introduction To Sub Riemannian Geometry books, Provides a comprehensive and self-contained introduction to sub-Riemannian geometry and its applications. For graduate students and researchers.




Sub Riemannian Geometry And Optimal Transport

Sub Riemannian Geometry and Optimal Transport PDF
Author: Ludovic Rifford
Publisher: Springer Science & Business Media
ISBN: 331904804X
Size: 65.38 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 140
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Sub Riemannian Geometry And Optimal Transport

by Ludovic Rifford, Sub Riemannian Geometry And Optimal Transport Books available in PDF, EPUB, Mobi Format. Download Sub Riemannian Geometry And Optimal Transport books, 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.




Sub Riemannian Geometry

Sub Riemannian Geometry PDF
Author: Ovidiu Calin
Publisher:
ISBN: 9781107104143
Size: 60.17 MB
Format: PDF, Kindle
Category : Electronic books
Languages : en
Pages : 384
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Sub Riemannian Geometry

by Ovidiu Calin, Sub Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Sub Riemannian Geometry books, A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.




Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning

Control of Nonholonomic Systems  from Sub Riemannian Geometry to Motion Planning PDF
Author: Frédéric Jean
Publisher: Springer
ISBN: 3319086901
Size: 14.26 MB
Format: PDF
Category : Science
Languages : en
Pages : 104
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Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning

by Frédéric Jean, Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning Books available in PDF, EPUB, Mobi Format. Download Control Of Nonholonomic Systems From Sub Riemannian Geometry To Motion Planning books, 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.




An Introduction To The Heisenberg Group And The Sub Riemannian Isoperimetric Problem

An Introduction to the Heisenberg Group and the Sub Riemannian Isoperimetric Problem PDF
Author: Luca Capogna
Publisher: Springer Science & Business Media
ISBN: 3764381337
Size: 42.93 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 224
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An Introduction To The Heisenberg Group And The Sub Riemannian Isoperimetric Problem

by Luca Capogna, An Introduction To The Heisenberg Group And The Sub Riemannian Isoperimetric Problem Books available in PDF, EPUB, Mobi Format. Download An Introduction To The Heisenberg Group And The Sub Riemannian Isoperimetric Problem books, 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.




Geometry Analysis And Dynamics On Sub Reimannian Manifolds

Geometry  Analysis and Dynamics on Sub Reimannian Manifolds PDF
Author: Davide Barilari
Publisher:
ISBN: 9783037191620
Size: 36.43 MB
Format: PDF, Docs
Category : Geometry, Differential
Languages : en
Pages : 332
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Geometry Analysis And Dynamics On Sub Reimannian Manifolds

by Davide Barilari, Geometry Analysis And Dynamics On Sub Reimannian Manifolds Books available in PDF, EPUB, Mobi Format. Download Geometry Analysis And Dynamics On Sub Reimannian Manifolds books, Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is allowed only along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds. In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology. The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.




Topics In Sub Riemannian Geometry

Topics in Sub Riemannian Geometry PDF
Author:
Publisher:
ISBN:
Size: 42.69 MB
Format: PDF, Docs
Category :
Languages : en
Pages :
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Topics In Sub Riemannian Geometry

by , Topics In Sub Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Topics In Sub Riemannian Geometry books, Abstract: Sub-Riemannian geometry is the geometry of spaces with non- holonomic constraints. This paper presents an informal survey of some topics in this area, starting with the construction of geodesic curves and ending with a recent definition of curvature. Bibliography: 28 titles.