Schwarzian Derivatives and Uniform Local Univalence

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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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Complex Variables, 30C99, 31A05, 30C55

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http://salesiana.dossiersoluciones.com/handle/123456789/134104

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0706.4296
 http://arxiv.org/abs/0706.4296

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arXiv