# Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian

Magdalena Sobczak-Kneć; Viktor Starkov; Jan Szynal

Annales UMCS, Mathematica (2011)

- Volume: 65, Issue: 2, page 191-202
- ISSN: 2083-7402

## Access Full Article

top## Abstract

top## How to cite

topMagdalena Sobczak-Kneć, Viktor Starkov, and Jan Szynal. "Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian." Annales UMCS, Mathematica 65.2 (2011): 191-202. <http://eudml.org/doc/267533>.

@article{MagdalenaSobczak2011,

abstract = {The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.},

author = {Magdalena Sobczak-Kneć, Viktor Starkov, Jan Szynal},

journal = {Annales UMCS, Mathematica},

keywords = {Planar harmonic mappings; order of a linear invariant family; Jacobian; harmonic mapping; linear invariant family; order; affine invariant family},

language = {eng},

number = {2},

pages = {191-202},

title = {Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian},

url = {http://eudml.org/doc/267533},

volume = {65},

year = {2011},

}

TY - JOUR

AU - Magdalena Sobczak-Kneć

AU - Viktor Starkov

AU - Jan Szynal

TI - Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian

JO - Annales UMCS, Mathematica

PY - 2011

VL - 65

IS - 2

SP - 191

EP - 202

AB - The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.

LA - eng

KW - Planar harmonic mappings; order of a linear invariant family; Jacobian; harmonic mapping; linear invariant family; order; affine invariant family

UR - http://eudml.org/doc/267533

ER -

## References

top- Bshouty, D., Hengartner, W., Univalent harmonic mappings in the plane, Ann. Univ. Mariae Curie-Skłodowska Sect. A 48 (1994), 13-42.
- Duren, P., Harmonic Mappings in the Plane, Cambridge University Press, Cambridge, 2004. Zbl1055.31001
- Godula, J., Liczberski, P. and Starkov, V. V., Order of linearly invariant mappings in Cn, Complex Variables Theory Appl. 42 (2000), 89-96. Zbl1026.32032
- Pommerenke, Ch., Linear-invariante Familien analytischer Funktionen I, Math. Annalen 155 (1964), 108-154. Zbl0128.30105
- Schaubroeck, L. E., Subordination of planar harmonic functions, Complex Variables Theory Appl. 41, (2000), 163-178. Zbl1020.30021
- Sheil-Small, T., Constants for planar harmonic mappings, J. London Math. Soc. 42 (1990), 237-248. Zbl0731.30012

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.