On the nodal line of the second eigenfunction of the Laplacian over some concave domains in ${\mathbb{R}}^2$

Abstract

In this paper we will prove the nodal line $N$ of the second eigenfunction of the Laplacian over some simply connected concave domain $\Omega$ in ${\mathbb{R}}^2$ must intersect the boundary $\partial \Omega$ at exactly two points.

arXiv comment7 pages, 12 conference