Generic spectral simplicity of polygons

Details Generic spectral simplicity of polygons Generic spectral simplicity of polygons

2007-03-21

arxiv.org/abs/math/0703616v3

Mathematics

Spectral Theory

length reduced to 6 pages, 1 figure

Scientific paper

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.

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