Download or read book Geometry of Harmonic Maps written by Yuanlong Xin and published by Springer Science & Business Media. This book was released on 1996-04-30 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.
Download or read book Geometry of Harmonic Maps written by Yuanlong Xin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.
Download or read book The Analysis of Harmonic Maps and Their Heat Flows written by Fanghua Lin and published by World Scientific. This book was released on 2008 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Fourth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on August 8-11, 2007. The Meeting focused on experimental tests of these fundamental symmetries and on important theoretical issues, including scenarios for possible relativity violations. Experimental subjects covered include: astrophysical observations, clock-comparison measurements, cosmological birefringence, electromagnetic resonant cavities, gravitational tests, matter interferometry, muon behavior, neutrino oscillations, oscillations and decays of neutral mesons, particle-antiparticle comparisons, post-Newtonian gravity, space-based missions, spectroscopy of hydrogen and antihydrogen, and spin-polarized matter.Theoretical topics covered include: physical effects at the level of the Standard Model, General Relativity, and beyond; the possible origins and mechanisms for Lorentz and CPT violations; and associated issues in field theory, particle physics, gravity, and string theory. The contributors consist of the leading experts in this very active research field.
Download or read book Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1992 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.
Download or read book Harmonic Maps and Minimal Immersions with Symmetries written by James Eells and published by Princeton University Press. This book was released on 1993 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Download or read book Harmonic Mappings Between Riemannian Manifolds written by Jürgen Jost and published by . This book was released on 1984 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reflection Groups and Invariant Theory written by Richard Kane and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years.
Download or read book Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and published by Routledge. This book was released on 2018-05-04 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.
Download or read book Two Reports On Harmonic Maps written by James Eells and published by World Scientific. This book was released on 1995-03-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.
Download or read book Calculus of Variations and Harmonic Maps written by Hajime Urakawa and published by American Mathematical Soc.. This book was released on 2013-02-15 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods. The first part of the book is devoted to explaining the notion of (infinite-dimensional) manifolds and contains many examples. An introduction to Morse theory of Banach manifolds is provided, along with a proof of the existence of minimizing functions under the Palais-Smale condition. The second part, which may be read independently of the first, presents the theory of harmonic maps, with a careful calculation of the first and second variations of the energy. Several applications of the second variation and classification theories of harmonic maps are given.
Download or read book Harmonic Maps Selected Papers By James Eells And Collaborators written by James Eells and published by World Scientific. This book was released on 1992-08-21 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.
Download or read book Harmonic Morphisms Harmonic Maps and Related Topics written by Christopher Kum Anand and published by CRC Press. This book was released on 1999-10-13 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.
Download or read book Harmonic Mappings Twistors And Sigma Models written by Paul Gauduchon and published by World Scientific. This book was released on 1988-10-01 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic mappings have played in recent years and will likely to play in the future an important role in Differential Geometry and Theoretical Physics, where they are known as s-models. These Proceedings develop both aspects of the theory, with a special attention to the constructive methods, in particular the so-called twistorial approach. It includes expository articles on the twistorial methods, the various appearence of σ-models in Physics, the powerful analytic theory of regularity of SCHOEN-UHLENBECK.
Download or read book Harmonic Maps and Minimal Immersions with Symmetries AM 130 Volume 130 written by James Eells and published by Princeton University Press. This book was released on 2016-03-02 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Download or read book Harmonic Maps Between Riemannian Polyhedra written by James Eells and published by Cambridge University Press. This book was released on 2001-07-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.
Download or read book Handbook of Teichm ller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 888 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.
Download or read book Several Complex Variables written by Michael Schneider and published by Cambridge University Press. This book was released on 1999 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
