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}
}
  • Antonio Alarcón, Franc Forstnerič
  • 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

    Citations

    Publications citing this paper.
    SHOWING 1-2 OF 2 CITATIONS