Displaying similar documents to “On a question of T. Sheil-Small regarding valency of harmonic maps”

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.

On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition

Agnieszka Sibelska (2010)

Annales UMCS, Mathematica

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The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri...

Harmonic deformability of planar curves

Eleutherius Symeonidis (2021)

Commentationes Mathematicae Universitatis Carolinae

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We study the formerly established concept of deformation of a planar curve and clarify its applicability and range. We present several applications on classical curves.

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.