Injectivity Criteria for Holomorphic Curves in $\mathbb{C}^n$
Complex Variables
2009-06-16 v1 Differential Geometry
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 . The result can be considered a generalization of a classical condition for univalence of Nehari.
Cite
@article{arxiv.0906.2776,
title = {Injectivity Criteria for Holomorphic Curves in $\mathbb{C}^n$},
author = {M. Chuaqui and P. Duren and B. Osgood},
journal= {arXiv preprint arXiv:0906.2776},
year = {2009}
}