# Complete densely embedded complex lines in $\mathbb{C}^2$

@article{Alarcn2017CompleteDE,
title={Complete densely embedded complex lines in \$\mathbb\{C\}^2\$},
author={Antonio Alarc{\'o}n and Franc Forstneri{\vc}},
journal={arXiv: Complex Variables},
year={2017},
pages={1}
}
• Published 2017
• Materials Science, Physics, Mathematics
• arXiv: Complex Variables
• In this paper we construct a complete injective holomorphic immersion $\mathbb{C}\to\mathbb{C}^2$ whose image is dense in $\mathbb{C}^2$. The analogous result is obtained for any closed complex submanifold $X\subset \mathbb{C}^n$ for $n>1$ in place of $\mathbb{C}\subset\mathbb{C}^2$. We also show that, if $X$ intersects the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ and $K$ is a connected compact subset of $X\cap\mathbb{B}^n$, then there is a Runge domain $\Omega\subset X$ containing $K$ which… CONTINUE READING

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