Fueter regular mappings and harmonicity

Wiesław Królikowski

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CONTENTSIntroduction........................................................................................................6I. Quaternionic regular and biregular functions in the sense of Fueter..............9 1. Introduction................................................................................................9 2. Fueter derivative and regular functions.....................................................10 3. Quaternionic partial derivatives.................................................................12 4....

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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...

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On Dyakonov type theorems for harmonic quasiregular mappings

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We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.