## Prove the Inverse of a Nonconstant Harmonic Function is Unbounded

Let u be a nonconstant harmonic function on C. Show that for any c∈R,u−1(c) is unbounded. Hint: {|z|>R} is connected for any R>0. It seems like this proof might require some sort of a “trick”, because I’m not sure how to attack this one directly. I know what I want to show is that for … Read more