Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings
Complex Variables
2019-05-01 v2 Differential Geometry
Abstract
For analytic functions in the unit disk, general bounds on the Schwarzian derivative in terms of Nehari functions are shown to imply uniform local univalence and in some cases finite and bounded valence. Similar results are obtained for the Weierstrass--Enneper lifts of planar harmonic mappings to their associated minimal surfaces. Finally certain classes of harmonic mappings are shown to have finite Schwarzian norm.
Keywords
Cite
@article{arxiv.math/0607067,
title = {Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings},
author = {M. Chuaqui and P. Duren and B. Osgood},
journal= {arXiv preprint arXiv:math/0607067},
year = {2019}
}