Affine and linear invariant families of harmonic mappings
Chuaqui
M
author
Hernandez
R
author
Martin
M
J
author
2017
English
We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk. By using the famous shear construction of Clunie and Sheil-Small, we construct a function to determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class S-H of univalent harmonic mappings can be formulated as a question about Schwarzian norm and, in particular, our result shows consistency between the conjectured order of S-H and the Schwarzian norm of the harmonic Koebe function.
WOS:000398175700006
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text
10.1007/s00208-016-1418-x
Chuaqui_etal2017
Mathematische Annalen
Math. Ann.
2017
Springer Heidelberg
continuing
periodical
academic journal
367
3-4
1099
1122
0025-5831