Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings
arXiv:math/0607067 · doi:10.1017/S0305004107000394
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.
Cited by in corpus (8)
- Sufficient conditions for univalence of analytic functions
- On singular Sturm theorems
- Optimization of relative arbitrage
- Some properties of univalent log-harmonic mappings
- Schwarzian Derivatives and Uniform Local Univalence
- Quasiconformal Extensions to Space of Weierstrass-Enneper Lifts
- Pre-Schwarzian and Schwarzian derivatives of harmonic mappings
- Criteria for bounded valence of harmonic mappings