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
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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
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