A nonconstant holomorphic function cannot attain a local maximum of its modulus in the interior.Suggest a slogan
Let \(\Omega\subseteq\CC\) be a connected open set and let \(f\colon \Omega \to \CC\) be holomorphic and nonconstant. Then \(\abs{f}\) attains no local maximum in \(\Omega\).
State the maximum modulus principle.