Harmonic Morphisms, Harmonic Maps and Related Topics
Christopher Kum Anand, Paul Baird, John Colin Wood, Eric Loubeau
CRC Press, Oct 13, 1999 - Mathematics - 328 pages
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.
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Harmonic morphisms via deformation of metrics for horizontally con
On the stability of harmonic morphisms
On the construction of harmonic morphisms from Euclidean spaces
Harmonic polynomial morphisms and Milnor fibrations
Quasiharmonic maps between almost symplectic manifolds
A discrete analogue of the harmonic morphism
Timedependent conservation laws and symmetries for classical
Harmonic maps and morphisms from spheres and deformed spheres
Harmonic extensions of quasiconformal maps to hyperbolic space
Harmonic sequences of harmonic 2surfaces in Grassmann manifolds
Gaugetheoretic equations for symmetric spaces and certain minimal
Moduli spaces of solutions to the gaugetheoretic equations
3-space 4-manifold Baird bundle compact complex structure conformal map constant mean curvature coordinates Corollary critical points defined Definition deformation denote dilation Eells equivalent erists Euclidean example exists fibration fibres finite gauge gauge-theoretic equations Gauss map Geom Geometry given graph harmonic functions harmonic maps harmonic morphism hence Hermitian manifolds Hermitian structure holomorphic map holomorphic with respect horizontally conformal map horizontally weakly Kähler manifold Lemma Lie algebra Lie group loop groups M_(M map f map ºp mean curvature minimal surfaces moduli space non-constant harmonic morphism obtain open subset orthogonal orthonormal polynomial principal bundle Proof Proposition quasi-harmonic Remark representation formula resp result Riemann surface Riemannian manifolds Riemannian metric Riemannian submersion satisfies sequence smooth map solution spacelike surface spheres subbundle submanifold submersive harmonic morphism subspace symplectic tamed manifold Theorem vector field vertical Willmore surfaces