2 problems

Let $\Omega \subset \mathbb{R}^2$ be a $C^\infty$ simply connected domain, and let $\mu^\Omega(E)$ be the first eigenvalue of the auxiliary operator $H_E^\Omega$. Let $\mathbb{D}$…

Bhattacharya–Weitsman–Nadirashvili conjecture. There exists a dimensional constant $C>0$ such that