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Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem
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Book Synopsis Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem by : Stefan P. Ivanov
Download or read book Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem written by Stefan P. Ivanov and published by World Scientific. This book was released on 2011 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to give an account of some important new developments in the study of the Yamabe problem on quaternionic contact manifolds. This book covers the conformally flat case of the quaternionic Heisenberg group or sphere, where complete and detailed proofs are given, together with a chapter on the conformal curvature tensor introduced very recently by the authors. The starting point of the considered problems is the well-known Folland?Stein Sobolev type embedding and its sharp form that is determined based on geometric analysis. This book also sits at the interface of the generalization of these fundamental questions motivated by the Carnot?Caratheodory geometry of quaternionic contact manifolds, which have been recently the focus of extensive research motivated by problems in analysis, geometry, mathematical physics and the applied sciences. Through the beautiful resolution of the Yamabe problem on model quaternionic contact spaces, the book serves as an introduction to this field for graduate students and novice researchers, and as a research monograph suitable for experts as well.
Book Synopsis Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem by :
Download or read book Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem by : A. L. Carey
Download or read book Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem written by A. L. Carey and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.
Book Synopsis Nonlinear Problems with Lack of Compactness by : Giovanni Molica Bisci
Download or read book Nonlinear Problems with Lack of Compactness written by Giovanni Molica Bisci and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-08 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
Download or read book Hokkaido Mathematical Journal written by and published by . This book was released on 2013 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic Analysis and Partial Differential Equations by : Michael Ruzhansky
Download or read book Harmonic Analysis and Partial Differential Equations written by Michael Ruzhansky and published by Springer Nature. This book was released on 2023-03-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers related to the session “Harmonic Analysis and Partial Differential Equations” held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.
Book Synopsis Advances in Harmonic Analysis and Partial Differential Equations by : Vladimir Georgiev
Download or read book Advances in Harmonic Analysis and Partial Differential Equations written by Vladimir Georgiev and published by Springer Nature. This book was released on 2020-11-07 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.
Book Synopsis Quaternionic Contact by : Stefan P. Ivanov
Download or read book Quaternionic Contact written by Stefan P. Ivanov and published by . This book was released on 2014 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 231, number 1086 (third of 5 numbers), September 2014."
Book Synopsis Hardy Spaces on Homogeneous Groups by : Gerald B. Folland
Download or read book Hardy Spaces on Homogeneous Groups written by Gerald B. Folland and published by Princeton University Press. This book was released on 1982-06-21 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.
Book Synopsis An Introduction to Contact Topology by : Hansjörg Geiges
Download or read book An Introduction to Contact Topology written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2008-03-13 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
Book Synopsis Nonlinear Analysis on Manifolds. Monge-Ampère Equations by : Thierry Aubin
Download or read book Nonlinear Analysis on Manifolds. Monge-Ampère Equations written by Thierry Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.
Book Synopsis Handbook of Global Analysis by : Demeter Krupka
Download or read book Handbook of Global Analysis written by Demeter Krupka and published by Elsevier. This book was released on 2011-08-11 with total page 1243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis , dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry. - Comprehensive coverage of modern global analysis and geometrical mathematical physics- Written by world-experts in the field- Up-to-date contents
Book Synopsis Stratified Lie Groups and Potential Theory for Their Sub-Laplacians by : Andrea Bonfiglioli
Download or read book Stratified Lie Groups and Potential Theory for Their Sub-Laplacians written by Andrea Bonfiglioli and published by Springer Science & Business Media. This book was released on 2007-08-24 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.
Book Synopsis Heat Kernels for Elliptic and Sub-elliptic Operators by : Ovidiu Calin
Download or read book Heat Kernels for Elliptic and Sub-elliptic Operators written by Ovidiu Calin and published by Springer Science & Business Media. This book was released on 2010-10-10 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.
Book Synopsis Spectral Theory, Function Spaces and Inequalities by : B. Malcolm Brown
Download or read book Spectral Theory, Function Spaces and Inequalities written by B. Malcolm Brown and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operator theory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
Book Synopsis Geometric and Computational Spectral Theory by : Alexandre Girouard
Download or read book Geometric and Computational Spectral Theory written by Alexandre Girouard and published by American Mathematical Soc.. This book was released on 2017-10-30 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS and Centre de Recherches Mathématiques The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Séminaire de Mathématiques Supérieures on Geometric and Computational Spectral Theory, held from June 15–26, 2015, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.
Book Synopsis Asymptotically Symmetric Einstein Metrics by : Olivier Biquard
Download or read book Asymptotically Symmetric Einstein Metrics written by Olivier Biquard and published by American Mathematical Soc.. This book was released on 2006 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence. In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence betweenEinstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book. Two new constructions of such Einstein metrics are given, using two different kinds of techniques: analytic methods toconstruct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis; algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary.
