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.
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. Brandao 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 Kahler 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. Riviere 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. Helein Effect of Topology on H-Surfaces, Y. Ge
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