Schwarzian derivative criteria for valence of analytic and harmonic mappings
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Date
2007
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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.