If f : 𝔻 → 𝔻 is holomorphic with f(0)=0, then |f(z)| ≤ |z| and |f'(0)| ≤ 1; equality anywhere forces f(z) = e^{iθ}z. Rigidifies holomorphic maps of the disc.
If f : 𝔻 → 𝔻 is holomorphic with f(0)=0, then |f(z)| ≤ |z| and |f'(0)| ≤ 1; equality anywhere forces f(z) = e^{iθ}z. Rigidifies holomorphic maps of the disc.