3 problems

Let $\Omega$ be a bounded convex domain, and suppose that it admits a finite-volume quotient. No regularity assumption is imposed on $\partial\Omega$. Bounded convex finite-volume…

Let $G$ be a compact subgroup of $O(n)$. A bounded, regular region $\Omega\subset\mathbb{R}^n$ is $G$-symmetric when it is invariant under the natural action of $G$. For an eigenva…

Let $G$ be a compact subgroup of $O(n)$, and let a region of $\mathbb{R}^n$ be $G$-symmetric when it is invariant under the natural action of $G$. The Dirichlet integral defines a…