let $f \colon G\to {\mathbb C}\ mathbb{C}$ $ be holomorphic and$z_0$some interior point of$G$. By the Poisson-Formula,$f(z_0)$is essentially the mean of values of$f$on a circle around$z_0$. Thus,$|f(z_0)|$is not maximal. 2 added 37 characters in body Maximum Principle for holomorphic functions: if let$f \colon G\to \mathbb{C}$be holomorphic and$z_0$is some interior point of the domain of$f$, by G$. By the Poisson-Formula, $f(z_0)$ is essentially the mean of values of $f$ on a circle around $z_0$. Thus, $|f(z_0)|$ is not maximal.
if $z_0$ is some interior point of the domain of $f$, by the Poisson-Formula, $f(z_0)$ is essentially the mean of values of a circle around $z_0$. Thus, $|f(z_0)|$ is not maximal.