Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/geometric-properties-of-harmonic-shears-ZUBqiaDLAP
References (10)
-
D. Bshouty, W. Hengartner (1997)
Boundary values versus dilatations of harmonic mappingsJournal d’Analyse Mathematique, 72
-
D Bshouty, W Hengartner (1997)
Boundary values versus dilatations of harmonic mappingsJ. Analyse Math., 12
-
W. Hengartner, G. Schober (1986)
Harmonic Mappings with Given DilatationJournal of The London Mathematical Society-second Series
-
W. Hengartner, G. Schober (1986)
On the boundary behavior of orientation-preserving harmonic mappingsComplex Variables and Elliptic Equations, 5
-
R. Laugesen (1997)
Planar Harmonic Maps with Inner and Blaschke DilatationsJournal of the London Mathematical Society, 56
-
C. Pommerenke (1992)
Boundary Behaviour of Conformal Maps -
P Duren, D Khavinson (1997)
Boundary correspondence and dilatation of harmonic mappingsComplex Variables Theory Appl., 33
-
W Hengartner, G Schober (1986)
On the boundary behavior of orientation-preserving harmonic mappingsComplex Variables Theory Appl., 5
-
J. Clunie, T. Sheil‐Small (1984)
Harmonic univalent functions, 9
-
P. Duren, D. Khavinson (1997)
Boundary correspondence and dilatation of harmonic mappingsComplex Variables and Elliptic Equations, 33
- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Heldermann Verlag
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/BF03321057
- Publisher site
- See Article on Publisher Site
Abstract
This paper is a study of planar harmonic mappings produced with the “shear construction” devised by Clunie and Sheil-Small in 1984. Specifically it will describe the geometry of mappings produced by the shear construction. The first section introduces basic concepts, including a description of the shear construction itself, a technique for constructing examples of harmonic mappings by shearing a conformal mapping. The main body of the paper alternates between presenting examples of harmonic shears, illustrating them graphically with the help of Mathematica software, and using an integral representation of the harmonic shear to explain and predict characteristics of the image domain.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Mar 7, 2013