Generic Spectral Simplicity of Polygons

@inproceedings{HILLAIRET2007GenericSS,
  title={Generic Spectral Simplicity of Polygons},
  author={LUC HILLAIRET and Chris Hope Judge},
  year={2007}
}
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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References

Publications referenced by this paper.
Showing 1-7 of 7 references

Analysis on singular spaces, an appendix in Metric structures for Riemannian and non-Riemannian spaces by M

  • S. Semmes
  • Gromov, Progress in Mathematics,
  • 1999

Three-Dimensional Geometry and Topology

  • W. P. Thurston
  • 1997

Spectral simplicity for conically singular constant curvature surfaces

  • L. Hillairet, C. Judge
  • Perturbation theory for linear operators
  • 1995

Methods of mathematical physics I

  • R. CH Courant, D. Hilbert
  • 1989

Generic properties of eigenfunctions

  • K. Uhlenbeck
  • Amer. J. Math
  • 1976

Genericity of simple eigenvalues for elliptic PDE’s

  • J. H. Albert
  • Proc. Amer. Math. Soc
  • 1975

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