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arXiv · 0706.4296

Schwarzian Derivatives and Uniform Local Univalence

Martin Chuaqui·Peter Duren·Brad Osgood
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Abstract

Quantitative estimates are obtained for the (finite) valence of functions analytic in the unit disk with Schwarzian derivative that is bounded or of slow growth. A harmonic mapping is shown to be uniformly locally univalent with respect to the hyperbolic metric if and only if it has finite Schwarzian norm, thus generalizing a result of B. Schwarz for analytic functions. A numerical bound is obtained for the Schwarzian norms of univalent harmonic mappings.

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Martin Chuaqui, Peter Duren, Brad Osgood. 2007-07-16. Schwarzian Derivatives and Uniform Local Univalence. https://arxiv.org/abs/0706.4296

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