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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2009

Generic spectral simplicity of polygons

Résumé

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.

Dates et versions

hal-00345668 , version 1 (09-12-2008)

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Luc Hillairet, Chris Judge. Generic spectral simplicity of polygons. Proceedings of the American Mathematical Society, 2009, 137 (6), pp.2139--2145. ⟨hal-00345668⟩
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