3 problems

Let $\Omega$ be an exceptional domain in $\mathbb{R}^n$, and suppose that $\Omega$ is homeomorphic to a halfspace. Halfspace classification conjecture. Then $\Omega$ is a halfspace…

Let an exceptional domain in $\mathbb{R}^2$ be a domain supporting the overdetermined potential-theoretic problem considered in the paper, and let its genus be finite. The three ex…

Let $n>2$, and let an axially symmetric exceptional domain be an exceptional domain in $\mathbb{R}^n$ invariant under rotations about an axis and containing that axis. Nonexistence…