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Author : Enrico Giusti
Publisher : Springer
Page : 295 pages
File Size : 52,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540397168
Author : Centro internazionale matematico estivo
Publisher : C.I.M.E. Foundation Subseries
Page : 304 pages
File Size : 53,6 Mb
Release : 1985-11
Category : Mathematics
ISBN : UOM:39015015607669
Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 238 pages
File Size : 54,5 Mb
Release : 1993
Category : Mathematics
ISBN : 069110249X
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.
Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 240 pages
File Size : 46,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882502
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.
Author : Gábor Tóth (Ph. D.)
Publisher : Unknown
Page : 176 pages
File Size : 46,9 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018970650
Author : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 228 pages
File Size : 43,6 Mb
Release : 1995-03-29
Category : Mathematics
ISBN : 9789814502924
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. Contents:IntroductionOperations on Vector BundlesHarmonic MapsComposition PropertiesMaps into Manifolds of Nonpositive (≤ 0) CurvatureThe Existence Theorem for Riem N ≤ 0Maps into Flat ManifoldsHarmonic Maps between SpheresHolomorphic MapsHarmonic Maps of a SurfaceHarmonic Maps between SurfacesHarmonic Maps of Manifolds with Boundary Readership: Mathematicians and mathematical physicists. keywords:Harmonic Maps;Minimal Immersions;Totally Geodesic Maps;Kaehler Manifold;(1,1)-Geodesic Map;Dilatation;Nonpositive Sectional Curvature;Holomorphic Map;Teichmueller Map;Twistor Construction “… an interesting account of the progress made in the theory of harmonic maps until the year 1988 … this master-piece work will serve as an influence and good reference in the very active subject of harmonic maps both from the points of view of theory and applications.” Mathematics Abstracts
Author : Centro internazionale matematico estivo
Publisher : Springer
Page : 312 pages
File Size : 52,5 Mb
Release : 1985
Category : Mathematics
ISBN : UCSD:31822032919235
Author : Paul Gauduchon
Publisher : World Scientific
Page : 390 pages
File Size : 50,8 Mb
Release : 1988-10-01
Category : Mathematics
ISBN : 9789813201484
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.
Author : Paul Baird,John C. Wood
Publisher : Oxford University Press
Page : 540 pages
File Size : 47,9 Mb
Release : 2003
Category : Mathematics
ISBN : 0198503628
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Author : James Eells
Publisher : World Scientific
Page : 472 pages
File Size : 53,7 Mb
Release : 1992
Category : Mathematics
ISBN : 9810207042
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.
Author : James Eells
Publisher : World Scientific
Page : 452 pages
File Size : 49,8 Mb
Release : 1992-08-21
Category : Science
ISBN : 9789814506120
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. Contents:Harmonic Mappings of Riemannian Manifolds (1964)Énergie et Déformations en Géométrie Différentielle (1964)Variational Theory in Fibre Bundles (1965)Restrictions on Harmonic Maps of Surfaces (1976)The Surfaces of Delaunay (1987)Minimal Graphs (1979)On the Construction of Harmonic and Holomorphic Maps between Surfaces (1980)Deformations of Metrics and Associated Harmonic Maps (1981)A Conservation Law for Harmonic Maps (1981)Maps of Minimum Energy (1981)The Existence and Construction of Certain Harmonic Maps (1982)Harmonic Maps from Surfaces to Complex Projective Spaces (1983)Examples of Harmonic Maps from Disks to Hemispheres (1984)Variational Theory in Fibre Bundles: Examples (1983)Constructions Twistorielles des Applications Harmoniques (1983)Removable Singularities of Harmonic Maps (1984)On Equivariant Harmonic Maps (1984)Regularity of Certain Harmonic Maps (1984)Gauss Maps of Surfaces (1984)Minimal Branched Immersions into Three-Manifolds (1985)Twistorial Construction of Harmonic Maps of Surfaces into Four-Manifolds (1985)Certain Variational Principles in Riemannian Geometry (1985)Harmonic Maps and Minimal Surface Coboundaries (1987)Unstable Minimal Surface Coboundaries (1986)Harmonic Maps between Spheres and Ellipsoids (1990)On Representing Homotopy Classes by Harmonic Maps (1991) Readership: Researchers and students in differential geometry and topology and theoretical physicists. keywords:Harmonic Mapping;Energy;Holomorphic Map;First (Second) Variation of Energy;Minimal Immersion;Minimal Graph;Regularity of Maps;Removable Singularities“It is striking that the papers cut a wide swathe through mathematics, and this is a testimony to the fact that the author has influenced so many younger mathematicians, several of whom are represented here.”Mathematical Reviews
Author : Hajime Urakawa
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 48,8 Mb
Release : 2013-02-15
Category : Mathematics
ISBN : 9780821894132
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.
Author : Enrico Bombieri
Publisher : Princeton University Press
Page : 368 pages
File Size : 44,6 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881437
The description for this book, Seminar On Minimal Submanifolds. (AM-103), Volume 103, will be forthcoming.
Author : Christopher Kum Anand,Paul Baird,John Colin Wood,Eric Loubeau
Publisher : CRC Press
Page : 332 pages
File Size : 52,7 Mb
Release : 1999-10-13
Category : Mathematics
ISBN : 1584880325
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.
Author : Gábor Tóth
Publisher : Unknown
Page : 360 pages
File Size : 51,5 Mb
Release : 1984
Category : Mathematics
ISBN : STANFORD:36105032120474