Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary

Junehyuk Jung, Steve Zelditch

It is an open problem in general to prove that there exists a sequence of ${\Delta }_g$-eigenfunctions ${\varphi }_{j_k}$ on a Riemannian manifold $(M,g)$ for which the number $N({\varphi }_{j_k})$ of nod…