Some regularity theorems in riemannian geometry

Dennis M. Deturck; Jerry L. Kazdan

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Some properties and applications of harmonic mappings

J. H. Sampson (1978)

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On normal forms of Laplacian and its iterations in harmonic spaces

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Geometrical interpretation of solutions of certain PDEs.

Udrişte, C., Neagu, M. (1999)

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Convergence of riemannian manifolds with integral bounds on curvature. II

Deane Yang (1992)

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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...