Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings

Details Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings Schwarzian Derivative Criteria for Valence of Analytic and Harmonic Mappings

2006-07-03

arxiv.org/abs/math/0607067v2

Mathematics

Complex Variables

Scientific paper

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.

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