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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2015 • Question 6

Question

Math 6210 • Real Analysis Spring 2015 • Question 6

Let \(f\) be an automorphism of the unit disk \(|z|<1\). Assume that \(f\) fixes two points. Prove that \(f(z)=z\) for all \(z\) in the unit disk.

Raw LaTeX

Let \(f\) be an automorphism of the unit disk \(|z|<1\). Assume that
\(f\) fixes two points. Prove that \(f(z)=z\) for all \(z\) in the unit disk.

Topic Tags

Automorphism Groups and Biholomorphisms