On quasiconformal extension of harmonic mappings with nonzero pole
Comptes Rendus. MathématiqueLet $\Sigma _H^k(p)$ be the class of sense-preserving univalent harmonic mappings defined on the open unit disk $\mathbb{D}$ of the complex plane with a simple pole at $z=p \in (0,1)$ that have $k$-quasiconformal extensions ($0\le ...
Bhowmik, Bappaditya, Satpati, Goutam
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Distortion of area and dimension under quasiconformal mappings in the plane. [PDF]
Proc Natl Acad Sci U S A, 1993 Astala K.
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Triangular Ratio Metric Under Quasiconformal Mappings in Sector Domains [PDF]
Computational methods in Function Theory, 2020 The hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them.
O. Rainio, M. Vuorinen
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On certain quasiconformal and elliptic mappings [PDF]
Journal of Mathematical Analysis and Applications, 2020 Let D ‾ be the closure of the unit disk D in the complex plane C and g be a continuous function in D ‾ . In this paper, we discuss some characterizations of elliptic mappings f satisfying the Poisson's equation Δ f = g in D , and then establish some ...
Shaolin Chen, S. Ponnusamy
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Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative [PDF]
Archiv der Mathematik, 2014 We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended ...
R. Hernández, María J. Martín
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An Approach to Studying Quasiconformal Mappings on Generalized Grushin Planes [PDF]
, 2014 We demonstrate that the complex plane and a class of generalized Grushin planes $G_r$, where $r$ is a function satisfying specific requirements, are quasisymmetrically equivalent.
Colleen Ackermann
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Extremal plane quasiconformal mappings with given boundary values
, 1973 Publisher Summary This chapter discusses the quasiconformal self mappings f = f x of the unit disc E: |z| x denotes the complex dilatation of the mapping f . By continuation, f induces a homeomorphism of the boundary ∂E onto itself.
E. Reich, K. Strebel
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Quantitative characterization of the human retinotopic map based on quasiconformal mapping. [PDF]
Med Image Anal, 2022 Ta D, Tu Y, Lu ZL, Wang Y.
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Duality of capacities and Sobolev extendability in the plane. [PDF]
Complex Analysis Synerg, 2021 Zhang YR.
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On proper branched coverings and a question of Vuorinen. [PDF]
Bull Lond Math Soc, 2022 Kauranen A, Luisto R, Tengvall V.
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