Convolution and quasiconformal extension

1976 ◽  
Vol 51 (1) ◽  
pp. 99-104 ◽  
Author(s):  
Jan G. Krzyż
Keyword(s):  
Quasiconformal Extension

Univalence criterion and quasiconformal extension of holomorphic mappings

2012 ◽  
Vol 141 (1-2) ◽  
pp. 195-209 ◽  
Author(s):  
Hidetaka Hamada ◽  
Gabriela Kohr
Keyword(s):  
Holomorphic Mappings ◽  
Quasiconformal Extension ◽  
Univalence Criterion

scholarly journals A Remark on Polygonal Quasiconformal Maps

2001 ◽  
Vol 8 (4) ◽  
pp. 815-822
Author(s):  
S. L. Krushkal
Keyword(s):  
Half Plane ◽  
Quasiconformal Extension ◽  
Quasiconformal Maps ◽  
Long Time ◽  
Upper Half Plane

Abstract Given a quasisymmetric map , let 𝑓0 be an extremal quasiconformal extension of ℎ onto the upper half-plane 𝘜 = {𝑧 ∈ ℂ : 𝔍𝑧 > 0} whose dilatation 𝑘(𝑓0) = inf{𝑘(𝑓) : 𝑓|∂𝘜 = ℎ0} ≕ 𝑘(ℎ). Let 𝑘𝑛 be the minimal dilatation of polygonal quasiconformal maps 𝑓 : 𝘜 → 𝘜 satisfying 𝑓(𝑥𝑗) = ℎ(𝑥𝑗), 𝑗 = 1, 2, . . . , 𝑛, for any 𝑛 points of (vertices of 𝑛-gons). Already a long time ago, the question was posed whether 𝑘(ℎ) = sup 𝑘𝑛, where the supremum is taken over all possible 𝑛-gons of such kind. The answer is obtained (in the negative) for the case of quadrilaterals (𝑛 = 4). We show that in the case of pentagons (𝑛 = 5) the answer is also negative, i.e., there are quasisymmetric ℎ with 𝑘(ℎ) > sup 𝑘5.

Gluing of quasisymmetric imbeddings in the problem of quasiconformal extension

2004 ◽  
Vol 56 (6) ◽  
pp. 873-881
Author(s):  
V. V. Aseev ◽  
A. V. Sychev ◽  
A. V. Tetenov
Keyword(s):  
Quasiconformal Extension

scholarly journals Quasiconformal extension of harmonic mappings in the plane

2013 ◽  
Vol 38 ◽  
pp. 617-630 ◽  
Author(s):  
Rodrigo Hernández ◽  
María J. Martín
Keyword(s):  
Quasiconformal Extension ◽  
Harmonic Mappings

SOME AREA THEOREMS FOR ANALYTIC FUNCTIONS WITH A QUASICONFORMAL EXTENSION

1974 ◽  
Vol 23 (1) ◽  
pp. 110-121
Author(s):  
Ju E Alenicyn
Keyword(s):  
Analytic Functions ◽  
Quasiconformal Extension

scholarly journals Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

2014 ◽  
Vol 104 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Rodrigo Hernández ◽  
María J. Martín
Keyword(s):  
Schwarzian Derivative ◽  
Quasiconformal Extension ◽  
Harmonic Mappings

Grunsky inequalities and quasiconformal extension

2006 ◽  
Vol 152 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Samuel Krushkal ◽  
Reiner Kühnau
Keyword(s):  
Quasiconformal Extension ◽  
Grunsky Inequalities

scholarly journals Quasiconformal extension and univalency criteria.

1992 ◽  
Vol 39 (2) ◽  
pp. 163-172
Author(s):  
De Lin Tan
Keyword(s):  
Quasiconformal Extension

On the dilatation estimates for Beurling-Ahlfors quasiconformal extension

1987 ◽  
Vol 100 (4) ◽  
pp. 655-655
Author(s):  
De Lin Tan
Keyword(s):  
Quasiconformal Extension

scholarly journals Diameter problems for univalent functions with quasiconformal extension

1993 ◽  
Vol 16 (4) ◽  
pp. 679-686
Author(s):  
Paul Deiermann
Keyword(s):  
Univalent Function ◽  
Univalent Functions ◽  
Extremal Length ◽  
Quasiconformal Extension ◽  
Image Domain ◽  
Complementary Component

This paper utilizes the method of extremal length to study several diameter problems for functions conformal outside of a disc centered at the origin, with a standard normalization, which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the diameter of a complementary component of the image domain of a univalent function are extended. Applications to the transfinite diameters of families of non-overlapping functions and an extension of the Koebe one-quarter theorem are included.

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