What is an example of a nonconstant subharmonic function that attains a minimum?

Question

Let $D$ be a domain in $\mathbb{C}$.

What would be an example of a nonconstant subharmonic function that attains its minimum in the domain?

Answer 1

Pick any $z_0\in D$. Let $f(z) = |z - z_0|^2$.

Answer 2

What examples of subharmonic functions do you know? What have you tried? The easiest thing would be to find a rotation invariant function which is subharmonic, and increasing along the real line. You should be able to produce many such functions