Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem

Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem PDF

Author: Stefan P Ivanov

Publisher: World Scientific

Published: 2011-03-08

Total Pages: 238

ISBN-13: 9814465550

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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.

Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem

Quaternionic Contact Einstein Structures and the Quaternionic Contact Yamabe Problem PDF

Author: A. L. Carey

Publisher: American Mathematical Soc.

Published: 2014-08-12

Total Pages: 94

ISBN-13: 0821898434

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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.

Nonlinear Problems with Lack of Compactness

Nonlinear Problems with Lack of Compactness PDF

Author: Giovanni Molica Bisci

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-02-08

Total Pages: 290

ISBN-13: 3110652013

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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.

Harmonic Analysis and Partial Differential Equations

Harmonic Analysis and Partial Differential Equations PDF

Author: Michael Ruzhansky

Publisher: Springer Nature

Published: 2023-03-06

Total Pages: 241

ISBN-13: 3031243110

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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.

Advances in Harmonic Analysis and Partial Differential Equations

Advances in Harmonic Analysis and Partial Differential Equations PDF

Author: Vladimir Georgiev

Publisher: Springer Nature

Published: 2020-11-07

Total Pages: 317

ISBN-13: 3030582159

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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.

Hardy Spaces on Homogeneous Groups

Hardy Spaces on Homogeneous Groups PDF

Author: Gerald B. Folland

Publisher: Princeton University Press

Published: 1982-06-21

Total Pages: 302

ISBN-13: 9780691083100

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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.

An Introduction to Contact Topology

An Introduction to Contact Topology PDF

Author: Hansjörg Geiges

Publisher: Cambridge University Press

Published: 2008-03-13

Total Pages: 8

ISBN-13: 1139467956

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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.

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