Nonexistence of Courant-type nodal domain bounds for eigenfunctions of the Dirichlet-to-Neumann operator

Alberto Enciso, Angela Pistoia, Luigi Provenzano

Given a compact manifold $\mathcal{M}$ with boundary of dimension $n\ge 3$ and any integers $K$ and $N$, we show that there exists a metric on $\mathcal{M}$ for which the first $K$…