Injectivity Criteria for Holomorphic Curves in C<i><SUP>n</SUP></i>
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Date
2011
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Abstract
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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Holomorphic mapping, Schwarzian derivative, curvature