Affine and linear invariant families of harmonic mappings

Martin Chuaqui, Rodrigo Hernández, María J. Martín

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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 SH 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 SH and the Schwarzian norm of the harmonic Koebe function.

Original languageEnglish
Pages (from-to)1099-1122
Number of pages24
JournalMathematische Annalen
Volume367
Issue number3-4
DOIs
StatePublished - 1 Apr 2017

Keywords

  • 30C55

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