An embedding of {\bf C} in {\bf C}$^2$ with hyperbolic complement
Abstract
Let $X$ be a closed, $1$dimensional, complex subvariety of $\CC^2$ and let $\ol{\BB}$ be a closed ball in $\CC^2  X$. Then there exists a FatouBieberbach domain $\Omega$ with $X \subseteq \Omega \subseteq \CC^2  \ol{\BB}$ and a biholomorphic map $\Phi: \Omega \ra \CC^2$ such that $\CC^2  \Phi(X)$ is Kobayashi hyperbolic. As corollaries, there is an embedding of the plane in $\CC^2$ whose complement is hyperbolic, and there is a nontrivial FatouBieberbach domain containing any finite collection of complex lines.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1995
 arXiv:
 arXiv:math/9506211
 Bibcode:
 1995math......6211B
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Complex Variables