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Abstract: Quantitative estimates are obtained for the finite valence of functionsanalytic in the unit disk with Schwarzian derivative that is bounded or of slowgrowth. A harmonic mapping is shown to be uniformly locally univalent withrespect to the hyperbolic metric if and only if it has finite Schwarzian norm,thus generalizing a result of B. Schwarz for analytic functions. A numericalbound is obtained for the Schwarzian norms of univalent harmonic mappings.



Author: Martin Chuaqui, Peter Duren, Brad Osgood

Source: https://arxiv.org/







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