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Schwarzian Derivatives and Uniform Local Univalence(28 Jun 2007)
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Find related articles from these CiteULike users Find related articles with these CiteULike tags AbstractQuantitative 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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