Affine and linear invariant families of harmonic mappings

被引：9

作者：

Chuaqui, Martin ^{[1
]}

Hernandez, Rodrigo ^{[2
]}

Martin, Maria J. ^{[3
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Casilla 306, Santiago, Chile

[2] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Ave Padre Hurtado 750, Vina Del Mar, Chile

[3] Univ Eastern Finland, Dept Math & Phys, POB 111, Joensuu 80101, Finland

来源：

MATHEMATISCHE ANNALEN | 2017年 / 367卷 / 3-4期

基金：

芬兰科学院;

关键词：

ANALYTISCHER FUNKTIONEN; CONFORMAL-MAPS; SCHWARZIAN; DISTORTION;

D O I：

10.1007/s00208-016-1418-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1099 / 1122

页数：24

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