Browsing by Author "Osgood, B."

Now showing 1 - 3 of 3
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    Injectivity Criteria for Holomorphic Curves in Cn
    (2011) Chuaqui, M.; Duren, P.; Osgood, B.
    Combining the definition of Schwarzian derivative for conformal mappings between Riemannian manifolds given by Osgood and Stowe with that for parametrized curves in Euclidean space given by Ahlfors, we establish injectivity criteria for holomorphic curves phi : D -> C-n. The result can be considered a generalization of a classical condition for univalence of Nehari.
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    Quasiconformal extensions to space of Weierstrass-Enneper lifts
    (2018) Chuaqui Farrú, Martín Skandar; Duren, P.; Osgood, B.
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    Univalence criteria for lifts of harmonic mappings to minimal surfaces
    (2007) Chuaqui, M.; Duren, R.; Osgood, B.
    A general criterion in terms of the Schwarzian derivative is given for global univalence of the Weierstrass-Enneper lift of a planar harmonic mapping. Results on distortion and boundary regularity are also deduced. Examples are given to show that the criterion is sharp. The analysis depends on a generalized Schwarzian defined for conformal metrics and on a Schwarzian introduced by Ahlfors for curves. Convexity plays a central role.