3 problems

Regularity conjecture. The results presented in this section should hold true for $C^{1,1}$ surfaces.

Let a torus be the boundary surface on which its Neumann–Poincaré (NP) operator is defined. Miyanishi's conjecture. The NP operator on tori has infinitely many negative eigenvalues…

Let $\partial\Omega$ be a $C^{\infty}$ simply connected closed surface, let $\mathcal{K}_{\partial\Omega}$ be its Neumann–Poincaré operator, and let $\zeta(s)$ denote the Riemann z…