@TedShifrin Ok , lets take things from the beggining we i have that my $ f $ has a local maximum at $ a $ then by using the mean value property it follows that $ f $ is constant on some disc containing $ a $
Then we try to prove that its constant so we connect $ a $ with an other point in our domain with a path . What i dont get is why in the subsequenct disc ( for example the second step ) we get that at the center of which our functions attains a maximum ( or a local max)
I know the following classical maximum principle for harmonic functions:
If $\Omega \subset \mathbb{C}$ is open and connected and $u \in
C^2(\Omega)$ is harmonic, then
$u$ has maximum (or minimum) in $\Omega$ $\implies$ $u$ constant.
How can I prove that the theorem is true if the h...
