Pleijel's nodal domain theorem for free membranes
arXiv:0805.1553
Abstract
We prove an analogue of Pleijel's nodal domain theorem for piecewise analytic planar domains with Neumann boundary conditions. This confirms a conjecture made by Pleijel in 1956. The proof is a combination of Pleijel's original approach and an estimate due to Toth and Zelditch for the number of boundary zeros of Neumann eigenfunctions.
4 pages; to appear in the Proceedings of the AMS