Consider a map $w:D^2\rightarrow S^2$ that is $J$-holomorphic. We say that it's multiply covered it there exists a map $f:D^2\rightarrow D^2$ of degree $|d|>1$ and a map $w':D^2\rightarrow S^2$ such that $w=w'\circ f$.
Now I have seen a result saying that if $w$ is not multiply covered then it's bijective in the interior of $D^2$. I have tried proving this going by contradiction and trying to create the actual map but I got nowhere. Does anyone know if this is actually true and how can we prove it?
Also could we generalize this for manifolds , or is it specific to this example?
Thanks in advance.