3 problems

Let $\Omega$ range over planar domains with regular boundary, and let $\operatorname{Pl}(\Delta^D_\Omega)$ and $\operatorname{Pl}(\Delta^N_\Omega)$ denote the Pleijel constants for…

Let $(\phi_n)$ be a sequence of Laplace eigenfunctions, and let $\mu(\phi_n)$ denote the number of nodal domains of $\phi_n$. Let $Sq_1$ be the square of area $1$, with first eigen…

Hexagonal conjecture for Pleijel.