2 problems

Let $\xi(D)=\lambda_2(D)/\lambda_1(D)$ be the fundamental ratio of the first two Dirichlet–Laplacian eigenvalues. Consider the moduli space of triangles after quotienting by the sy…

Let $P_k\subset\mathbb{R}^2$ be an open $k$-gon, and let $P_k^*\subset\mathbb{R}^d$ be an open regular $k$-gon. For $k\geq 3$, define the fundamental ratio by…