Suppose $U$ is a bounded open set in $\mathbb{R}^m$ with ($m\geq2$). Is it possible to have a non-empty set $E$ in the boundary $ \partial U$ of $U$ that is open in $ \partial U$ and is polar?
A set $E$ is called polar if there exists a superharmonic function on an open neighborhood of $E$ that takes the value of $\infty$ at each point of $E$.