3 problems

Let $f_1$ be the first eigenfunction of the biharmonic operator on the rectangle considered in the paper, with aspect parameter $h$ and constants $c$ and $d$ as defined there. Writ…

Let $R_a$ be a rectangle of unit area, parametrized by its side-length ratio $a\geq 1$, and let $\lambda_1(a)$ denote the first eigenvalue of the Dirichlet biharmonic operator on…

Let $N\in\mathbb N$ be fixed. Consider the biharmonic operator with Neumann boundary conditions on a hyperbolic ball in $\mathbb H^n$, and denote its eigenvalues by $\mu_j$. Hyperb…