English

Generic spectral simplicity of polygons

Spectral Theory 2008-02-19 v3

Abstract

We study the Laplace operator with Dirichlet or Neumann boundary condition on polygons in the Euclidean plane. We prove that almost every simply connected polygon with at least four vertices has simple spectrum. We also address the more general case of geodesic polygons in a constant curvature space form.

Keywords

Cite

@article{arxiv.math/0703616,
  title  = {Generic spectral simplicity of polygons},
  author = {Luc Hillairet and Chris Judge},
  journal= {arXiv preprint arXiv:math/0703616},
  year   = {2008}
}

Comments

length reduced to 6 pages, 1 figure