Grunsky inequalities and quasiconformal extension

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

Convolution and quasiconformal extension

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

Formulas for the Nehari Coefficients of Bounded Univalent Functions

1977 ◽  
Vol 29 (3) ◽  
pp. 587-605
Author(s):  
Duane W. De Temple ◽  
David B. Oulton
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Bieberbach Conjecture ◽  
Grunsky Inequalities

The Grunsky inequalities [6] and their generalizations (e.g., [5; 14; 17]) have become an increasingly important tool for the study of the coefficients of normalized univalent functions defined on the unit disc. In particular, proofs based upon the Grunsky inequalities have now settled the Bieberbach conjecture for the fifth [15] and sixth [13] coefficients. For bounded univalent functions the situation is similar, although the Grunsky inequalities go over to those of Nehari [11].

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

scholarly journals Fredholm spectrum and Grunsky inequalities in general domains

1986 ◽  
Vol 83 (2) ◽  
pp. 167-200
Author(s):  
Jacob Burbea
Keyword(s):  
Grunsky Inequalities
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