Geometry Of Biharmonic Mappings Differential Geometry Of Variational Methods

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Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods

Hajime Urakawa
Geometry Of Biharmonic Mappings Differential Geometry Of Variational Methods Book PDF

Author : Hajime Urakawa
Publisher : World Scientific
Page : 349 pages
File Size : 55,7 Mb
Release : 2018-12-06
Category : Mathematics
ISBN : 9789813236417

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Geometry Of Biharmonic Mappings: Differential Geometry Of Variational Methods by Hajime Urakawa Pdf

'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer’s opinion, this excellent monograph will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods.'zbMATHThe author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.

Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry

Ye-lin Ou,Bang-yen Chen
Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry Book PDF

Author : Ye-lin Ou,Bang-yen Chen
Publisher : World Scientific
Page : 541 pages
File Size : 53,9 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811212390

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Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry by Ye-lin Ou,Bang-yen Chen Pdf

The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.

Harmonic Vector Fields

Sorin Dragomir,Domenico Perrone
Harmonic Vector Fields Book PDF

Author : Sorin Dragomir,Domenico Perrone
Publisher : Elsevier
Page : 529 pages
File Size : 42,5 Mb
Release : 2011-10-26
Category : Computers
ISBN : 9780124158269

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Harmonic Vector Fields by Sorin Dragomir,Domenico Perrone Pdf

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods

Geometry of Harmonic Maps

Yuanlong Xin
Geometry of Harmonic Maps Book PDF

Author : Yuanlong Xin
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240846

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Geometry of Harmonic Maps by Yuanlong Xin Pdf

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.

Harmonic Maps and Minimal Immersions with Symmetries

James Eells,Andrea Ratto
Harmonic Maps and Minimal Immersions with Symmetries Book PDF

Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 238 pages
File Size : 41,8 Mb
Release : 1993
Category : Mathematics
ISBN : 069110249X

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Harmonic Maps and Minimal Immersions with Symmetries by James Eells,Andrea Ratto Pdf

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.

Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130

James Eells,Andrea Ratto
Harmonic Maps and Minimal Immersions with Symmetries AM 130 Volume 130 Book PDF

Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 240 pages
File Size : 44,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882502

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Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 by James Eells,Andrea Ratto Pdf

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.

Variational Methods in Lorentzian Geometry

Antonio Masiello
Variational Methods in Lorentzian Geometry Book PDF

Author : Antonio Masiello
Publisher : Routledge
Page : 166 pages
File Size : 48,9 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9781351405706

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Variational Methods in Lorentzian Geometry by Antonio Masiello Pdf

Appliies variational methods and critical point theory on infinite dimenstional manifolds to some problems in Lorentzian geometry which have a variational nature, such as existence and multiplicity results on geodesics and relations between such geodesics and the topology of the manifold.

Introduction to Global Variational Geometry

Demeter Krupka
Introduction to Global Variational Geometry Book PDF

Author : Demeter Krupka
Publisher : Elsevier
Page : 500 pages
File Size : 40,5 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080954286

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Introduction to Global Variational Geometry by Demeter Krupka Pdf

This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces

Differential Geometry of Varieties with Degenerate Gauss Maps

Maks A. Akivis,Vladislav V. Goldberg
Differential Geometry of Varieties with Degenerate Gauss Maps Book PDF

Author : Maks A. Akivis,Vladislav V. Goldberg
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 50,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387215112

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Differential Geometry of Varieties with Degenerate Gauss Maps by Maks A. Akivis,Vladislav V. Goldberg Pdf

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

Yuan-Jen Chiang
Developments of Harmonic Maps Wave Maps and Yang Mills Fields into Biharmonic Maps Biwave Maps and Bi Yang Mills Fields Book PDF

Author : Yuan-Jen Chiang
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 51,6 Mb
Release : 2013-06-18
Category : Mathematics
ISBN : 9783034805346

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Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields by Yuan-Jen Chiang Pdf

Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Harmonic Maps and Differential Geometry

Eric Loubeau,Stefano Montaldo
Harmonic Maps and Differential Geometry Book PDF

Author : Eric Loubeau,Stefano Montaldo
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 55,7 Mb
Release : 2011
Category : Geometry, Differential
ISBN : 9780821849873

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Harmonic Maps and Differential Geometry by Eric Loubeau,Stefano Montaldo Pdf

This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.

Differential Geometry, Calculus of Variations, and Their Applications

George M. Rassias,Themistocles M. Rassias
Differential Geometry Calculus of Variations and Their Applications Book PDF

Author : George M. Rassias,Themistocles M. Rassias
Publisher : CRC Press
Page : 550 pages
File Size : 44,9 Mb
Release : 1985-10-01
Category : Mathematics
ISBN : 0824772679

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Differential Geometry, Calculus of Variations, and Their Applications by George M. Rassias,Themistocles M. Rassias Pdf

This book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.

Harmonic Mappings, Twistors And Sigma Models

Paul Gauduchon
Harmonic Mappings Twistors And Sigma Models Book PDF

Author : Paul Gauduchon
Publisher : World Scientific
Page : 390 pages
File Size : 44,5 Mb
Release : 1988-10-01
Category : Mathematics
ISBN : 9789813201484

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Harmonic Mappings, Twistors And Sigma Models by Paul Gauduchon Pdf

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.

Two Reports on Harmonic Maps

James Eells,Luc Lemaire
Two Reports on Harmonic Maps Book PDF

Author : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 38 pages
File Size : 53,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9810214669

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Two Reports on Harmonic Maps by James Eells,Luc Lemaire Pdf

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, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and K„hlerian 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.

Handbook of Differential Geometry, Volume 1

F.J.E. Dillen,L.C.A. Verstraelen
Handbook of Differential Geometry Volume 1 Book PDF

Author : F.J.E. Dillen,L.C.A. Verstraelen
Publisher : Elsevier
Page : 1067 pages
File Size : 49,8 Mb
Release : 1999-12-16
Category : Mathematics
ISBN : 9780080532837

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Handbook of Differential Geometry, Volume 1 by F.J.E. Dillen,L.C.A. Verstraelen Pdf

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.