Let $f\colon \mathbb{C}\to \mathbb{C}$ be a nonconstant entire function.
Is it true that there exists $\bar{f}\colon S^2\to S^2$ with $\bar{f}|_\mathbb{C}=f$?
Let $f\colon \mathbb{C}\to \mathbb{C}$ be a nonconstant entire function.
Is it true that there exists $\bar{f}\colon S^2\to S^2$ with $\bar{f}|_\mathbb{C}=f$?