English

Affine and linear invariant families of harmonic mappings

Complex Variables 2014-05-21 v1

Abstract

We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class SH\mathcal{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 SH\mathcal{S}_H and the Schwarzian norm of the harmonic Koebe function.

Keywords

Cite

@article{arxiv.1405.5106,
  title  = {Affine and linear invariant families of harmonic mappings},
  author = {Martin Chuaqui and Rodrigo Hernández and María José Martín},
  journal= {arXiv preprint arXiv:1405.5106},
  year   = {2014}
}