Displaying similar documents to “Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian”

Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian

Magdalena Sobczak-Kneć, Viktor V. Starkov, Jan Szynal (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.

On Dyakonov type theorems for harmonic quasiregular mappings

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.

Harmonic mappings onto parallel slit domains

Michael Dorff, Maria Nowak, Magdalena Wołoszkiewicz (2011)

Annales Polonici Mathematici

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We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.

Harmonic morphisms between riemannian manifolds

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism f : M N between Riemannian manifolds M and N is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim M 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...