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Author : Davide Barilari
Publisher :
ISBN 13 : 9783037196632
Total Pages : pages
Book Rating : 4.1/5 (966 download)
Download or read book Geometry, Analysis and Dynamics on Sub-Reimannian Manifolds written by Davide Barilari and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Davide Barilari
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (17 download)
Download or read book Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds written by Davide Barilari and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Davide Barilari
Publisher : European Mathematical Society
ISBN 13 : 9783037191637
Total Pages : 312 pages
Book Rating : 4.1/5 (916 download)
Download or read book Geometry, Analysis and Dynamics on Sub-Reimannian Manifolds written by Davide Barilari and published by European Mathematical Society. This book was released on 2016 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Davide Barilari
Publisher :
ISBN 13 : 9783037196625
Total Pages : 332 pages
Book Rating : 4.1/5 (966 download)
Download or read book Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds written by Davide Barilari and published by . This book was released on 2016 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed 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.
Author : Ovidiu Calin
Publisher : Cambridge University Press
ISBN 13 : 0521897300
Total Pages : 371 pages
Book Rating : 4.5/5 (218 download)
Download or read book Sub-Riemannian Geometry written by Ovidiu Calin and published by Cambridge University Press. This book was released on 2009-04-20 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
Author : Andre Bellaiche
Publisher : Birkhäuser
ISBN 13 : 3034892101
Total Pages : 404 pages
Book Rating : 4.0/5 (348 download)
Download or read book Sub-Riemannian Geometry written by Andre Bellaiche and published by Birkhäuser. This book was released on 2012-12-06 with total page 404 pages. 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.
Author : Andrei Agrachev
Publisher : Cambridge University Press
ISBN 13 : 110847635X
Total Pages : 765 pages
Book Rating : 4.1/5 (84 download)
Download or read book A Comprehensive Introduction to Sub-Riemannian Geometry written by Andrei Agrachev and published by Cambridge University Press. This book was released on 2019-10-31 with total page 765 pages. 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.
Author : Ana Hurtado
Publisher : Springer Nature
ISBN 13 : 3030552934
Total Pages : 121 pages
Book Rating : 4.0/5 (35 download)
Download or read book Global Riemannian Geometry: Curvature and Topology written by Ana Hurtado and published by Springer Nature. This book was released on 2020-08-19 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.
Author : John Bland
Publisher : American Mathematical Soc.
ISBN 13 : 0821832735
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)
Download or read book Explorations in Complex and Riemannian Geometry written by John Bland and published by American Mathematical Soc.. This book was released on 2003 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.
Author : Bruno Bianchini
Publisher : Springer Nature
ISBN 13 : 3030627047
Total Pages : 291 pages
Book Rating : 4.0/5 (36 download)
Download or read book Geometric Analysis of Quasilinear Inequalities on Complete Manifolds written by Bruno Bianchini and published by Springer Nature. This book was released on 2021-01-18 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Author : Andrei Agrachev
Publisher : Cambridge University Press
ISBN 13 : 1108757251
Total Pages : 765 pages
Book Rating : 4.1/5 (87 download)
Download or read book A Comprehensive Introduction to Sub-Riemannian Geometry written by Andrei Agrachev and published by Cambridge University Press. This book was released on 2019-10-31 with total page 765 pages. 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.
Author : Ovidiu Calin
Publisher :
ISBN 13 : 9781107104143
Total Pages : 384 pages
Book Rating : 4.1/5 (41 download)
Download or read book Sub-Riemannian Geometry written by Ovidiu Calin and published by . This book was released on 2009 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.
Author : Steven Rosenberg
Publisher : Cambridge University Press
ISBN 13 : 9780521468312
Total Pages : 190 pages
Book Rating : 4.4/5 (683 download)
Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg and published by Cambridge University Press. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Author : Fabrice Baudoin
Publisher : Springer Nature
ISBN 13 : 3030841413
Total Pages : 312 pages
Book Rating : 4.0/5 (38 download)
Download or read book New Trends on Analysis and Geometry in Metric Spaces written by Fabrice Baudoin and published by Springer Nature. This book was released on 2022-02-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes four courses on geometric measure theory, the calculus of variations, partial differential equations, and differential geometry. Authored by leading experts in their fields, the lectures present different approaches to research topics with the common background of a relevant underlying, usually non-Riemannian, geometric structure. In particular, the topics covered concern differentiation and functions of bounded variation in metric spaces, Sobolev spaces, and differential geometry in the so-called Carnot–Carathéodory spaces. The text is based on lectures presented at the 10th School on "Analysis and Geometry in Metric Spaces" held in Levico Terme (TN), Italy, in collaboration with the University of Trento, Fondazione Bruno Kessler and CIME, Italy. The book is addressed to both graduate students and researchers.
Author : Stefano Pigola
Publisher : Springer Science & Business Media
ISBN 13 : 3764386428
Total Pages : 282 pages
Book Rating : 4.7/5 (643 download)
Download or read book Vanishing and Finiteness Results in Geometric Analysis written by Stefano Pigola and published by Springer Science & Business Media. This book was released on 2008-05-28 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory.
Author : Ovidiu Calin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821843192
Total Pages : 264 pages
Book Rating : 4.8/5 (431 download)
Download or read book Geometric Analysis on the Heisenberg Group and Its Generalizations written by Ovidiu Calin and published by American Mathematical Soc.. This book was released on 2007 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of subRiemannian manifolds is closely related to Hamiltonian mechanics. In this book, the authors examine the properties and applications of subRiemannian manifolds that automatically satisfy the Heisenberg principle, which may be useful in quantum mechanics. In particular, the behavior of geodesics in this setting plays an important role in finding heat kernels and propagators for Schrodinger's equation. One of the novelties of this book is the introduction of techniques from complex Hamiltonian mechanics. Information for our distributors: Titles in this series are co-published with International Press, Cambridge, MA.
Author : Olga Gil-Medrano
Publisher : Springer Nature
ISBN 13 : 3031368576
Total Pages : 131 pages
Book Rating : 4.0/5 (313 download)
Download or read book The Volume of Vector Fields on Riemannian Manifolds written by Olga Gil-Medrano and published by Springer Nature. This book was released on 2023-07-31 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs. A wide range of topics is covered, including: a discussion on the conditions for a vector field on a Riemannian manifold to determine a minimal submanifold within its tangent bundle with the Sasaki metric; numerous examples of minimal vector fields (including those of constant length on punctured spheres); a thorough analysis of Hopf vector fields on odd-dimensional spheres and their quotients; and a description of volume-minimizing vector fields of constant length on spherical space forms of dimension three. Each chapter concludes with an up-to-date survey which offers supplementary information and provides valuable insights into the material, enhancing the reader's understanding of the subject. Requiring a solid understanding of the fundamental concepts of Riemannian geometry, the book will be useful for researchers and PhD students with an interest in geometric analysis.
