A note on harmonic maps between surfaces

Jürgen Jost

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On the existence of harmonic maps from a surface into the real projective plane

Jürgen Jost (1986)

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Twistorial construction of harmonic maps of surfaces into four-manifolds

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Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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An energy estimate of an exterior problem and a Liouville theorem for harmonic maps

Dong Zhang (1994)

Annales de l'I.H.P. Analyse non linéaire

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Harmonic morphisms onto Riemann surfaces and generalized analytic functions

Paul Baird (1987)

Annales de l'institut Fourier

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We study harmonic morphisms from domains in $R^{3}$ and $S^{3}$ to a Riemann surface $N$ , obtaining the classification of such in terms of holomorphic mappings from a covering space of $N$ into certain Grassmannians. We show that the only non-constant submersive harmonic morphism defined on the whole of $S^{3}$ to a Riemann surface is essentially the Hopf map. Comparison is made with the theory of analytic functions. In particular we consider multiple-valued harmonic morphisms defined on domains...

Heat flow and boundary value problem for harmonic maps

Chang Kung-Ching (1989)

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Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

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A harmonic morphism $f : M \to N$ between Riemannian manifolds $M$ and $N$ is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim $M \geq$ dim $N$ , since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where $d f$ vanishes. Every non-constant harmonic morphism is shown to be...