# [Complex Analysis] prove non-existence of conformal map

## Homework Statement

"Show that there is no conformal map from D(0,1) to \mathbb C"
and D(0,1) means the (open) unit disk

## Homework Equations

Conformal maps preserve angles

## The Attempt at a Solution

I don't have a clue. I thought the clou might be that D(0,1) has a boundary, and C doesn't, so I tried to draw some circles/lines on D(0,1) that couldn't be imaged onto C whilst preserving angles, but to no avail.

## Answers and Replies

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Dick
Homework Helper
I'm guessing you mean a bijective function. Then the inverse map would map C to D(0,1). Think about what you might conclude from that.

Last edited:
Oh, does a conformal map have to be bijective?

(in that case: the inverse would be bounded ==(Liouville)==> constant, contradiction)
(Now I'm also assuming differentiability! So does a conformal map have to be bijective AND/OR analytical?)

Dick