Payne's nodal line conjecture fails on doubly-connected planar domains
arXiv:2510.24436
Abstract
We present examples of bounded planar domains with one single hole for which the nodal line of a second Dirichlet eigenfunction is closed and does not touch the boundary. This shows that Payne's nodal line conjecture can at most hold for simply-connected domains in the plane.
13 pages, including 5 figures and the appendix