A Picard type theorem for quasiregular mappings of R into n-manifolds with many ends.
Ilkka Holopainen, Seppo Rickman (1992)
Revista Matemática Iberoamericana
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Ilkka Holopainen, Seppo Rickman (1992)
Revista Matemática Iberoamericana
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B. Johnson (1973)
Studia Mathematica
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Miloš Arsenović, Miroslav Pavlović (2017)
Czechoslovak Mathematical Journal
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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.
Petrunin, Anton (2003)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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S. Hartman (1975)
Colloquium Mathematicae
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A. Calderón, A. Zygmund (1964)
Studia Mathematica
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Kilpeläinen, Tero (1994)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Jevtić, M. (1995)
Publications de l'Institut Mathématique. Nouvelle Série
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S. Simić (1979)
Matematički Vesnik
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Tapanidis, T., Tsagas, Gr., Mazumdar, H.P. (2000)
Balkan Journal of Geometry and its Applications (BJGA)
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Bent Fuglede (1978)
Annales de l'institut Fourier
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A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, 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 vanishes. Every non-constant harmonic morphism is shown to be...