Let \(A_R=\{z\in \mathbb {C}\mid 1<|z|<R\}\) for \(R>1\). If \(A_R\) and \(A_{R'}\) are biholomorphic, show that \(R=R'\).
Question
Math 6220 • Complex Analysis
Fall 2025 • Question 6
Question
Fall 2025 • Question 6
Let \(A_R=\{z\in \mathbb {C}\mid 1<|z|<R\}\) for \(R>1\). If \(A_R\) and \(A_{R'}\) are biholomorphic, show that \(R=R'\).