Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian
Magdalena Sobczak-Kneć; Viktor V. Starkov; Jan Szynal
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2011)
- Volume: 65, Issue: 2
- ISSN: 0365-1029
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topMagdalena Sobczak-Kneć, Viktor V. Starkov, and Jan Szynal. "Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 65.2 (2011): null. <http://eudml.org/doc/289847>.
@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 V. Starkov, Jan Szynal},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {Planar harmonic mappings; order of a linear invariant family; Jacobian},
language = {eng},
number = {2},
pages = {null},
title = {Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian},
url = {http://eudml.org/doc/289847},
volume = {65},
year = {2011},
}
TY - JOUR
AU - Magdalena Sobczak-Kneć
AU - Viktor V. Starkov
AU - Jan Szynal
TI - Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2011
VL - 65
IS - 2
SP - null
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
UR - http://eudml.org/doc/289847
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.
- Godula, J., Liczberski, P. and Starkov, V. V., Order of linearly invariant mappings in Cn, Complex Variables Theory Appl. 42 (2000), 89-96.
- Pommerenke, Ch., Linear-invariante Familien analytischer Funktionen I, Math. Annalen 155 (1964), 108-154.
- Schaubroeck, L. E., Subordination of planar harmonic functions, Complex Variables Theory Appl. 41, (2000), 163-178.
- Sheil-Small, T., Constants for planar harmonic mappings, J. London Math. Soc. 42 (1990), 237-248.
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