Geodesic
Harmonic mappings in the exterior of the unit disk
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 54 (2010) no. 1

Voir la notice de l'article provenant de la source Library of Science

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition∑_n=1^∞n^p(|a_n|+|b_n|)≤ 1. We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.
Keywords: Harmonic mapping, meromorphic, quasiconformal extension, radius of convexity, radius of univalence 
Gregorczyk, Magdalena; Widomski, Jarosław. Harmonic mappings in the exterior of the unit disk. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 54 (2010) no. 1. http://geodesic.mathdoc.fr/item/AUM_2010_54_1_a1/
@article{AUM_2010_54_1_a1,
     author = {Gregorczyk, Magdalena and Widomski, Jaros{\l}aw},
     title = {Harmonic mappings in the exterior of the unit disk},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica},
     year = {2010},
     volume = {54},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2010_54_1_a1/}
}
TY  - JOUR
AU  - Gregorczyk, Magdalena
AU  - Widomski, Jarosław
TI  - Harmonic mappings in the exterior of the unit disk
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica
PY  - 2010
VL  - 54
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUM_2010_54_1_a1/
LA  - en
ID  - AUM_2010_54_1_a1
ER  - 
%0 Journal Article
%A Gregorczyk, Magdalena
%A Widomski, Jarosław
%T Harmonic mappings in the exterior of the unit disk
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica
%D 2010
%V 54
%N 1
%U http://geodesic.mathdoc.fr/item/AUM_2010_54_1_a1/
%G en
%F AUM_2010_54_1_a1

[1] Hengartner W., Schober G., Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31.

[2] Jahangiri, Jay M., Harmonic meromorphic starlike functions, Bull. Korean Math. Soc. 37 (2000), No. 2, 291-301.

[3] Jahangiri, Jay M., Silverman H., Meromorphic univalent harmonic functions with

[4] negative coefficients, Bull. Korean Math. Soc. 36 (1999), No. 4, 763-770.

[5] Lehto O., Virtanen K. I., Quasiconformal Mappings in the Plane, Springer-Verlag, Berlin-Heidelberg-New York, Second Edition, 1973.

[6] Pommerenke Ch., Univalent Functions, Vandenhoeck Ruprecht in Gottingen, 1975.

[7] Sheil-Small T., Complex Polynomials, Cambridge University Press, 2002.