Harmonic diffeomorphisms, minimizing harmonic maps and rotational symmetry

J. M. Coron; F. Helein

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On the biharmonicity of product maps.

Todjihounde, Leonard (2006)

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On generalized $f$ -harmonic morphisms

A. Mohammed Cherif, Djaa Mustapha (2014)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study the characterization of generalized $f$ -harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an $f$ -harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144],...

$f$ -harmonic maps which map the boundary of the domain to one point in the target.

Course, Neil (2007)

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Inequalities involving multipliers for multivalent harmonic functions.

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On weakly harmonic maps and Noether harmonic maps from a Riemann surface into a Riemannian manifold

Frédéric Hélein (1992)

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The boundary value problem for Dirac-harmonic maps

Qun Chen, Jürgen Jost, Guofang Wang, Miaomiao Zhu (2013)

Journal of the European Mathematical Society

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Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian...

Harmonic mappings into manifolds with boundary

Yun Mei Chen, Roberta Musina (1990)

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Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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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...