Displaying similar documents to “Boundary correspondence under quasiconformal harmonic diffeomorphisms of a half-plane.”

Harmonic mappings in the exterior of the unit disk

Jarosław Widomski, Magdalena Gregorczyk (2010)

Annales UMCS, Mathematica

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In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings

David Kalaj (2011)

Studia Mathematica

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We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.

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 in the exterior of the unit disk

Magdalena Gregorczyk, Jarosław Widomski (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition ∑ n = 1 ∞ n p ( | a n | + | b n | ) ≤ 1 . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.