Holomorphic function on a unbounded domain
I have problem in understanging the following question
Q. Show by means of an example that a non-constant holomorphic function on a n unbounded domain need not achieve it's maximum modulus on the boundary of that domain
Answer: here we assume that tha boundary is not empty.
Maximum Modulus Principle says that
"|f(z)| can only achieve its maximum value on the boundary unless it is constant"
So i am wondering how can i connect the MMP with the above question.
Any help will be appreciated....Thanks