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 isinjectiveon .

Anybody can help?

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- March 31st 2011, 03:53 PMEinStoneInjectivity of Holomorphic function
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? - March 31st 2011, 04:45 PMDrexel28
- March 31st 2011, 10:55 PMEinStone
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.

- March 31st 2011, 11:14 PMDrexel28
There is a proof in this book, page 26.