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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

2001 • Question 10

Question

Math 6210 • Real Analysis 2001 • Question 10

Assume that \(f\) is a one-to-one conformal mapping of the open disc \(|z|<1\) onto a regular \(n\)-gon with center at \(0\), and \(f(0)=0\). Prove that \(f(\rho z)=\rho f(z)\) where \(\rho \) is any \(n\)-th root of \(1\). Remember that conformal maps preserve angles.

Raw LaTeX

Assume that \(f\) is a one-to-one conformal mapping of the open disc
\(|z|<1\) onto a regular \(n\)-gon with center at \(0\), and \(f(0)=0\). Prove that
\(f(\rho z)=\rho f(z)\) where \(\rho\) is any \(n\)-th root of \(1\). Remember that
conformal maps preserve angles.

Topic Tags

Automorphism Groups and Biholomorphisms Conformal Moduli and Annuli