Injectivity Criteria for Holomorphic Curves in $\mathbb{C}^n$

Details Injectivity Criteria for Holomorphic Curves in $\mathbb{C}^n$ Injectivity Criteria for Holomorphic Curves in $\mathbb{C}^n$

2009-06-15

arxiv.org/abs/0906.2776v1

Mathematics

Complex Variables

Scientific paper

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 $\phi:\mathbb{D}\to\mathbb{C}^n$. The result can be considered a generalization of a classical condition for univalence of Nehari.

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