2 problems

Fatou–Bieberbach approximation conjecture. For every $r\in(0,1)$, there exists a domain $\Omega_r\subseteq{\mathbb{C}^n}$ biholomorphic to ${\mathbb{C}^n}$ such that

Fatou–Bieberbach realization conjecture. There exists a Fatou–Bieberbach domain $\Omega\subseteq{\mathbb{C}^n}$ with $D\subseteq\Omega$ such that $(D,\Omega)$ is a Runge pair. This…