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Harmonic Morphisms, Harmonic Maps and Related Topics

Edited by Christopher Kum Anand, Paul Baird, John Colin Wood, Eric Loubeau

Series Editor: Blaine Lawson

Contributors: Paul Baird, B Fuglede, Xiaogun Mo, R Pantilie, S Montaldo, M T Mustafa, J C Wood, Y-L Ou, S Ianus, A M Pastore, C L Bejan, H Urakawa, C K Anand, Y-X Dong, E Sandier, M Soret, R Hardt, M Wolf, J-Y Chen, M Ville, J C Negreiros, P Topping, Y Ohnita, M Mukai, F Pacard, T Riviere, J-I Inoguchi, R Miyaoka, R Aiyama, K Akutagawa, F Helein, Y Ge

Published October 13th 1999 by Chapman and Hall/CRC – 328 pages

Series: Chapman & Hall/CRC Research Notes in Mathematics Series

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Description

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.

Contents

HARMONIC MORPHISMS

The Beginings of Harmonic Morphisms, B. Fuglede

Harmonic Morphisms via Deformation of Metrics for Horizontally Conformal Maps, X. Mo

On Submersive Harmonic Morphisms, R. Pantilie

On the Stability of Harmonic Morphisms, S. Montaldo

Applications of the Bachner Technique to Harmonic Morphisms between Simply-Connected Space Forms, M.T. Mustafa

On the Construction of Harmonic Morphisms from Euclidean Spaces, J.C. Wood

Harmonic Polynomial Morphisms and Milnor Fibrations, P. Baird and Y.-L. Ou

Harmonic Maps and Morphisms on Metric f-Manifolds with Paralellizable Kernel, S. Ianus and A.M. Pastore

Quasi-Harmonic Maps between Almost Symplectic Manifolds, P. Baird and C.L. Bejan

A Discrete Analogue of Harmonic Morphisms, H. Urakawa

Harmonic Morphisms of Metric Graphs, C.K. Anand

Time Dependent Conservation Laws and Symmetries for Classical Mechanics and Heat Equations, A. Brandão and T. Kolsrud

HARMONIC MAPS: GENERAL THEORY, MAPS OF SURFACES, AND RELATED VARIATIONAL PROBLEMS

Harmonic Maps and Morphisms from Spheres and Deformed Spheres,Y.-X. Dong

S1-Valued Harmonic Maps with High Topological Degree, E. Sandier and M. Soret

Harmonic Maps to Non-Locally Compact Spaces, R. Shoen

Harmonic Extensions of Quasi-Conformal Maps to Hyperbolic Space, R. Hardt and M. Wolf

Harmonic Mappings from Riemann Surfaces, J.-Y. Chen

On the Normal Bundle of Minimal Surfaces in Almost Kähler 4-Manifolds, M. Ville

Harmonic Sequences of Harmonic 2-Surfaces in Grassmann Manifolds, X. Mo and C.J.C. Negreiros

An Example of a Nontrivial Bubble Tree in the Harmonic Map Heat Flow, P. Topping

Gauge-Theoretic Equations for Symmetric Spaces and Certain Minimal Submanifolds in Moduli Spaces, Y. Ohnita

Moduli Spaces of Solutions to the Gauge Theoretic Equations for Harmonic Maps, M. Mukai

On the Set of Minimizers of the Ginzburg-Landau Functional in Dimension 2, F. Pacard and T. Rivière

CONSTANT MEAN CURVATURE SURFACES

Surfaces in Minkowski 3-Space and Harmonic Maps, J.-I. Inoguchi

The Splitting and Deformations of the Gauss Map of Compact C.M.C. Surfaces, R. Miyaoka

Representation Formulas for Surfaces in H3(-c2) and Harmonic Maps Arising from CMC Surfaces, R. Aiyama and K. Akutagawa

A Weierstrass Representation for Willmore Surfaces, F. Hélein

Effect of Topology on H-Surfaces, Y. Ge

Name: Harmonic Morphisms, Harmonic Maps and Related Topics (Paperback) – Chapman and Hall/CRC 
Description: Edited by Christopher Kum Anand, Paul Baird, John Colin Wood, Eric LoubeauSeries Editor: Blaine LawsonContributors: Paul Baird, B Fuglede, Xiaogun Mo, R Pantilie, S Montaldo, M T Mustafa, J C Wood, Y-L Ou, S Ianus, A M Pastore, C L Bejan, H Urakawa, C K Anand, Y-X Dong, E Sandier, M Soret, R Hardt, M Wolf, J-Y Chen, M Ville, J C Negreiros, P Topping, Y Ohnita, M Mukai, F Pacard, T Riviere, J-I Inoguchi, R Miyaoka, R Aiyama, K Akutagawa, F Helein, Y Ge. 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...
Categories: Geometry, Differential Equations