Let $M$ be a complex manifold which is homeomorphic to the disk $D:=|z|<1$, suppose that $m\in M$, define $M^*:=M\setminus \{m\}$. Then we can we show that $M^*$ and $D^*:=0<|z|<1$ are biholomorphic?
As someone pointed out, when $M=\mathbb{C}$ it is not true, but I wonder under what condition it is true and how to show that?