The Problem:

Suppose that is a simply connected domain with , , and for some (an open disk at a with radius r). For a unit disk, let be a conformal map with . Prove that .

Ideas:

- There is a drawing (.pdf) attached that represents the set context.

- Application of the Riemann Ext Thm. provides a conformal map from onto with and (or another suitable rotation) and a map from onto and .

- Seems like a setup for Schwarz's Lemma. For example, we can take with and . Then the lemma asserts that and . So . I don't see where this helps with this proof.

Thank you in advance for your help in solving this.