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

Author : Luca Capogna
Publisher : Springer Science & Business Media
ISBN 13 : 3764381337
Total Pages : 224 pages
Book Rating : 4.32/5 ( download)

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Download or read book An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem written by Luca Capogna and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 224 pages. 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.

Author : Luca Capogna
Publisher : Birkhäuser
ISBN 13 : 9783764391850
Total Pages : 224 pages
Book Rating : 4.55/5 ( download)

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Download or read book An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem written by Luca Capogna and published by Birkhäuser. This book was released on 2009-09-03 with total page 224 pages. 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.

Author : Andrei Agrachev
Publisher : Cambridge University Press
ISBN 13 : 110847635X
Total Pages : 765 pages
Book Rating : 4.55/5 ( download)

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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 : Antonio Alarcón
Publisher : Springer Nature
ISBN 13 : 3031399161
Total Pages : 398 pages
Book Rating : 4.69/5 ( download)

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Download or read book New Trends in Geometric Analysis written by Antonio Alarcón and published by Springer Nature. This book was released on 2023-11-25 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide an overview of some of the progress made by the Spanish Network of Geometric Analysis (REAG, by its Spanish acronym) since its born in 2007. REAG was created with the objective of enabling the interchange of ideas and the knowledge transfer between several Spanish groups having Geometric Analysis as a common research line. This includes nine groups at Universidad Autónoma de Barcelona, Universidad Autónoma de Madrid, Universidad de Granada, Universidad Jaume I de Castellón, Universidad de Murcia, Universidad de Santiago de Compostela and Universidad de Valencia. The success of REAG has been substantiated with regular meetings and the publication of research papers obtained in collaboration between the members of different nodes. On the occasion of the 15th anniversary of REAG this book aims to collect some old and new contributions of this network to Geometric Analysis. The book consists of thirteen independent chapters, all of them authored by current members of REAG. The topics under study cover geometric flows, constant mean curvature surfaces in Riemannian and sub-Riemannian spaces, integral geometry, potential theory and Riemannian geometry, among others. Some of these chapters have been written in collaboration between members of different nodes of the network, and show the fruitfulness of the common research atmosphere provided by REAG. The rest of the chapters survey a research line or present recent progresses within a group of those forming REAG. Surveying several research lines and offering new directions in the field, the volume is addressed to researchers (including postdocs and PhD students) in Geometric Analysis in the large.

Author : M. W. Wong
Publisher : Birkhäuser
ISBN 13 : 3319475126
Total Pages : 239 pages
Book Rating : 4.27/5 ( download)

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Download or read book Pseudo-Differential Operators: Groups, Geometry and Applications written by M. W. Wong and published by Birkhäuser. This book was released on 2017-01-20 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015. The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

Author : Giovanna Citti
Publisher : Birkhäuser
ISBN 13 : 3034804083
Total Pages : 170 pages
Book Rating : 4.80/5 ( download)

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Download or read book Harmonic and Geometric Analysis written by Giovanna Citti and published by Birkhäuser. This book was released on 2015-04-28 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an expanded version of lectures delivered by the authors at the CRM in Spring of 2009. It contains four series of lectures. The first one is an application of harmonic analysis and the Heisenberg group to understand human vision. The second and third series of lectures cover some of the main topics on linear and multilinear harmonic analysis. The last one is a clear introduction to a deep result of De Giorgi, Moser and Nash on regularity of elliptic partial differential equations in divergence form.

Author : Yuri Sachkov
Publisher : Springer Nature
ISBN 13 : 3031020707
Total Pages : 176 pages
Book Rating : 4.04/5 ( download)

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Download or read book Introduction to Geometric Control written by Yuri Sachkov and published by Springer Nature. This book was released on 2022-07-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is an enhanced, English version of the Russian edition, published in early 2021 and is appropriate for an introductory course in geometric control theory. The concise presentation provides an accessible treatment of the subject for advanced undergraduate and graduate students in theoretical and applied mathematics, as well as to experts in classic control theory for whom geometric methods may be introduced. Theory is accompanied by characteristic examples such as stopping a train, motion of mobile robot, Euler elasticae, Dido's problem, and rolling of the sphere on the plane. Quick foundations to some recent topics of interest like control on Lie groups and sub-Riemannian geometry are included. Prerequisites include only a basic knowledge of calculus, linear algebra, and ODEs; preliminary knowledge of control theory is not assumed. The applications problems-oriented approach discusses core subjects and encourages the reader to solve related challenges independently. Highly-motivated readers can acquire working knowledge of geometric control techniques and progress to studying control problems and more comprehensive books on their own. Selected sections provide exercises to assist in deeper understanding of the material. Controllability and optimal control problems are considered for nonlinear nonholonomic systems on smooth manifolds, in particular, on Lie groups. For the controllability problem, the following questions are considered: controllability of linear systems, local controllability of nonlinear systems, Nagano–Sussmann Orbit theorem, Rashevskii–Chow theorem, Krener's theorem. For the optimal control problem, Filippov's theorem is stated, invariant formulation of Pontryagin maximum principle on manifolds is given, second-order optimality conditions are discussed, and the sub-Riemannian problem is studied in detail. Pontryagin maximum principle is proved for sub-Riemannian problems, solution to the sub-Riemannian problems on the Heisenberg group, the group of motions of the plane, and the Engel group is described.

Author : Dorothea Bahns
Publisher : Birkhäuser
ISBN 13 : 3319224077
Total Pages : 314 pages
Book Rating : 4.77/5 ( download)

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Download or read book Quantization, PDEs, and Geometry written by Dorothea Bahns and published by Birkhäuser. This book was released on 2016-02-11 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary waves, and sub-Riemannian geometry. The contributions are based on lectures given by distinguished experts at a summer school in Göttingen. The authors explain fundamental concepts and ideas and present them clearly. Starting from basic notions, these course notes take the reader to the point of current research, highlighting new challenges and addressing unsolved problems at the interface between mathematics and physics. All contributions are of interest to researchers in the respective fields, but they are also accessible to graduate students.

Author : Vasileios Chousionis
Publisher : American Mathematical Soc.
ISBN 13 : 1470442159
Total Pages : 153 pages
Book Rating : 4.56/5 ( download)

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Download or read book Conformal Graph Directed Markov Systems on Carnot Groups written by Vasileios Chousionis and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

Author : Veronique Fischer
Publisher : Birkhäuser
ISBN 13 : 3319295586
Total Pages : 557 pages
Book Rating : 4.89/5 ( download)

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Download or read book Quantization on Nilpotent Lie Groups written by Veronique Fischer and published by Birkhäuser. This book was released on 2016-03-08 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.