## Harmonic Morphisms, Harmonic Maps and Related TopicsChristopher Kum Anand, Paul Baird, John Colin Wood, Eric Loubeau 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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### Contents

Harmonic morphisms via deformation of metrics for horizontally con | 13 |

On the stability of harmonic morphisms | 31 |

On the construction of harmonic morphisms from Euclidean spaces | 47 |

Harmonic polynomial morphisms and Milnor fibrations | 61 |

Quasiharmonic maps between almost symplectic manifolds | 75 |

A discrete analogue of the harmonic morphism | 97 |

Timedependent conservation laws and symmetries for classical | 113 |

Harmonic maps and morphisms from spheres and deformed spheres | 129 |

Harmonic extensions of quasiconformal maps to hyperbolic space | 147 |

Harmonic sequences of harmonic 2surfaces in Grassmann manifolds | 175 |

Gaugetheoretic equations for symmetric spaces and certain minimal | 193 |

Moduli spaces of solutions to the gaugetheoretic equations | 209 |

### Common terms and phrases

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