Selected topics in harmonic maps by James Eells

Cover of: Selected topics in harmonic maps | James Eells

Published by Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society in Providence, R.I .

Written in English

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Subjects:

  • Harmonic maps,
  • Geometry, Riemannian

Edition Notes

Book details

Statementby James Eells and Luc Lemaire.
SeriesRegional conference series in mathematics,, no. 50
ContributionsLemaire, Luc, 1950-, Conference Board of the Mathematical Sciences.
Classifications
LC ClassificationsQA1 .R33 no. 50, QA614.73 .R33 no. 50
The Physical Object
Paginationv, 85 p. ;
Number of Pages85
ID Numbers
Open LibraryOL3504887M
ISBN 100821807005
LC Control Number82025526

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Selected topics in harmonic maps. [James Eells; Luc Lemaire; Conference Board of the Mathematical Sciences.] Gives an account of the various aspects of the theory of harmonic maps between Riemannian manifolds.

This book presents an exposition of the qualitative aspects of harmonic maps. Selected Topics in Harmonic Maps Share this page James Eells; Luc Lemaire. A co-publication of the AMS and CBMS. The first part of the book is devoted to an account of various aspects of the theory of harmonic maps between Riemannian manifolds.

The second part proposes certain unsolved problems, together with comments and references, which are. Selected Topics in Harmonic Maps by James Eells,available at Book Depository with free delivery worldwide.

Selected Topics in Harmonic Maps: James Eells: We use cookies to give you the best possible experience. Buy Selected Topics in Harmonic Maps (Cbms Regional Conference Series in Mathematics) on FREE SHIPPING on qualified orders Selected Topics in Harmonic Maps (Cbms Regional Conference Series in Mathematics): James Eells and Luc 5/5(1).

Destination page number Search scope Search Text Search scope Search Text. Harmonic maps 13 3. Some properties of harmonic maps 21 4. Second Variation of the energy 27 5. Spheres and the behavior of the energy 32 6. The stress-energy tensor 38 7.

Harmonic morphisms 41 8. Holomorphic and harmonic maps between almost Kahler manifolds 47 9. Properties of harmonic maps between Kahler manifolds 53 Part II. Selected Topics in Harmonic Maps (Cbms Regional Conference Series in Mathematics) | James Eells and Luc Lemaire | download | B–OK.

Download books for free. Find books. Selected Topics in Harmonic Maps. 点击放大图片 出版社: American Mathematical Society. 作者: Eells, James; Lemaire, L. 出版时间: 年12月15 日. 10位国际标准书号: 13位国际标准.

♥ Book Title: Harmonic Maps Between Riemannian Polyhedra ♣ Name Author: J. Selected topics in harmonic maps book Eells ∞ Launching: Info ISBN Link: ⊗ Detail ISBN code: ⊕ Number Pages: Total sheet ♮ News id: 8pjRqy5EfoEC Download File Start Reading ☯ Full Synopsis: "A research level book on harmonic maps between singular spaces, by renowned authors, first published in   Harmonic maps between smooth Riemannian manifolds play a ubiquitous role in differential geometry.

Examples include geodesics viewed as maps, minimal surfaces, holomorphic maps and Abelian integrals viewed as maps to a circle. The theory of such maps has been extensively developed over the last 30 years, and has significant applications throughout mathematics. A (smooth) map:M→N between Riemannian manifolds M and N is called harmonic if it is a critical point of the Dirichlet energy functional = ∫ ‖ ‖.This functional E will be defined precisely below—one way of understanding it is to imagine that M is made of rubber and N made of marble (their shapes given by their respective metrics), and that the map:M→N prescribes how one "applies.

In this chapter, we follow the notions and notations of harmonic maps between Riemannian manifolds by Eells- Sampson [] in the discuss the crucial topics in harmonic maps including fundamentals, regularity, maps of surfaces, maps of K \(\ddot{a}\) hler manifolds, maps into groups and Grassmannians, harmonic maps, loop groups.

Elegant and concise, this text is geared toward advanced undergraduate students acquainted with the theory of functions of a complex variable.

The treatment presents such students with a number of important topics from the theory of analytic functions that may be addressed without erecting an elaborate superstructure.

These include some of the theory's most celebrated results, which. HARMONIC MORPHISMS BETWEEN RIEMANNIAN MANIFOLDS 3 Definition A continuous map ϕ: U → C from an open subset of Rm is called a harmonic morphism if, whenever h: V → R is a harmonic function on an open subset V of C with ϕ−1(V) non-empty, then h ϕ is by: The text demonstrates how the theory of loop groups can be used to study harmonic maps.

By concentrating on the main ideas and examples, the author leads up to topics of current research. The book is suitable for students who are beginning to study manifolds and Lie groups, and should be of interest both to mathematicians and to theoretical.

The specific goal of the book is to show how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the author leads up Author: Martin A. Guest.

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations.

InCaminha published a six-volume book collection entitled Topics in Elementary Mathematics with the Brazilian Mathematical Society, which gave rise to this book.

He also published a book on selected topics on Differential Geometry, especially the Bochner method and harmonic : Springer International Publishing. Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields (Frontiers in Mathematics) - Kindle edition by Chiang, Yuan-Jen.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Developments of Harmonic Maps, Wave Maps and Yang Manufacturer: Birkhäuser. Learning roadmap for harmonic analysis. Ask Question Asked 8 years, it would be nice to hear suggestions of some important topics in the subject of harmonic analysis that are current interests of research and references one could use to better understand these topics.

I would tackle this before moving onto Elias Stein's book "harmonic. Selected topics in harmonic maps, volume 50 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC, Some new Author: Marco Spinaci.

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.

[5] Eells J, Lemaire L. Selected Topics in Harmonic Maps. CBMS Regional Conference Series in Mathematics, vol. CBMS Regional Conference Series in. Get this from a library.

Selected papers on harmonic analysis, groups, and invariants. [Katsumi Nomizu;] -- This volume contains papers that originally appeared in Japanese in the journal Sūgaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication the.

Polyharmonic hypersurfaces into space forms. Selected topics in harmonic maps. CBMS Regional Conference Series in Mathematics, This book will be of use to graduate students and. Abstract. Let ψ:(M, g) → (N, h) be a map between Riemannian manifolds (M, g) and (N, h).We introduce the notion of the F-bienergy functional.

E F, 2 (ψ) = ∫ M F | τ (ψ) | 2 2 d V g. where F: [0, ∞) → [0, ∞) be C 3 function such that F ′ > 0 on (0, ∞), τ(ψ) is the tension field of al points of τ F,2 are called F-biharmonic this paper, we prove a Author: Rong Mi. Harmonic maps.

Title. 8 Additional Topics Harmonic Mappings of Annuli Multiply Connected Domains Most of the book concerns harmonic mappings in the plane, but there are occasional excursions into higher dimensions, if only to provide counter. Introduces students to the mathematical concepts arising in signal analysis from the applied harmonic analysis point of view.

Topics include applied linear algebra, Fourier series, discrete Fourier transform, Fourier transform, Shannon Sampling Theorem, wavelet bases, multiresolution analysis, and discrete wavelet transform.

RECTIFIABLE-REIFENBERG AND THE REGULARITY OF STATIONARY AND MINIMIZING HARMONIC MAPS AARON NABER AND DANIELE VALTORTA ABSTRACT. In this paper we study the regularity of stationary and minimizing harmonic maps f: B2(p) ⊆ M → N between Riemannian manifolds. If Sk(f) ≡ {x ∈ M: no tangent map at x is k + 1-symmetric} is the.

Abstract. This survey studies equivariant harmonic maps arising from Higgs bundles. We explain the non-abelian Hodge correspondence and focus on the role of equivariant harmonic maps in the correspondence.

With the preparation, we review current progress towards some open problems in the study of equivariant harmonic maps. The first book is pragmatically written and guides the reader to a lot of interesting stuff, like Hodge's theorem, Morse homology and harmonic maps.

The second book is mainly concerned with Cartan connection, but before that it has an excellent chapter on differential topology. Furthermore it treats Ehresmann connections in appendix A. CB CB/DUREN Janu Char Count= 0 1 Preliminaries Harmonic Mappings A real-valued function u(x, y)isharmonic if it satisfies Laplace’s equation: u = ∂2u ∂x2 ∂2u ∂y2 = 0.

A one-to-one mapping u = u(x, y),v= v(x, y) from a region D in the xy- plane to a region in the uv-plane is a harmonic mapping if the two coordi- nate functions are harmonic. Other books written by Eells on this topic were Selected topics in harmonic maps () with Luc Lemaire, Harmonic maps and minimal immersions with symmetries () with Andrea Ratto (another PhD student of Eells' who received his doctorate in ), and Harmonic maps between Riemannian polyhedra () with the Danish mathematician B Fuglede.

Harmonic generation by tightly-focused Gaussian beams is finding important applications, primarily in nonlinear microscopy. It is often naively assumed that the nonlinear signal is generated predominantly in the focal region.

However, the intensity of Gaussian-excited electromagnetic harmonic waves is sensitive to the excitation geometry and to the phase matching condition, and may depend on Cited by: 1. Eells did research on global analysis, especially, harmonic maps on Riemannian manifolds, which are important in the theory of minimal surfaces and theoretical physics.

His doctoral students included John C. Wood. In he was an invited speaker at the International Mathematical Congress in Nice (On Fredholm manifolds with K. Elworthy). Book Description. Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers.

The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. A study of f-harmonic maps and f-harmonic heat ow. The rst chapter gives the de nitions of f-harmonic maps and heat ow; namely the critical points of the energy functional Ef(u):= 1 2 R M fjruj2 dM (for a compact surface M) and the L2{gradient ow of this energy.

The rst and second variations of Ef are calculated, and previously known f-harmonicFile Size: KB. Geometry of Harmonic Maps This monograph examines a fundamental mathematical concept connected to differential Geometry - stochastic processes. Selected Topics in Harmonic Maps Theory of Matrices Theory of Named Sets Geometry of Cuts and Metrics.

PHILIP HARTMAN monic maps homotopicfœ are to obtained by a "rotationfœ" (i.e. of, by moving each poinfœt{x) afixed oriented distance u along 7) and, conversely, every "rotation offœ " is a harmonic map It should be noted that in (H) and (I) there are no curvature assumptions on M. This contrasts with the corollary of (1, p.

This collection covers all papers and partial talks given by Prof Weiyue Ding, who was a member of the Chinese Academy of Sciences. Prof Weiyue Ding devoted his academic career to the research in the field of ordinary differential equations and geometric analysis, e.g.

Poincaré–Birkhoff fixed point theorems, blow-up analysis for heat flow of harmonic maps. HARMONIC MAPPINGS OF RIEMANNIAN MANIFOLDS.

11 Chapter II. Deformations of maps. 6. Deformations by the heat equation 7. Global equations 8. Derivative bounds for the elliptic case 9. Bounds for the parabolic case Successive approximations Harmonic mappings Added in proof: The theory of the energy functional (and its harmonic.In a sense, Harmonic Analysis subsumes both his Fourier Analysis and Singular Integrals books, but I believe it assumes a lot of basic information on Fourier Analysis that his earlier book covers.

Another great and very modern book would be Wolff's Lecture Notes on Harmonic Analysis (available for .(with A. Freire and S. Müller) Weak compactness of wave maps and harmonic maps, Ann. Inst. H. Poincari, Analyse Non-Linéaire (), (with S.

Müller) Global existence of wave maps in 1+2 dimensions with finite energy data, Topological methods in nonlinear analysis 7 .

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