Let U be an open disk around the origin in .
Suppose is holomorphic on , and .
I want to show that there exists a neighborhood of , , so that is injective on .
Anybody can help?
Yes, it seems like a general statement for a holomorphic function to be locally invertible if it has non vanishing derivative. Something like an inverse function theorem, but I cant find it anywhere, if someone has a proof of this fact or a reference would be great.