Generic spectral simplicity of polygons
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- by Luc Hillairet and Chris Judge PDF
- Proc. Amer. Math. Soc. 137 (2009), 2139-2145 Request permission
Abstract:
We study the Laplace operator with Dirichlet or Neumann boundary conditions on polygons in the Euclidean plane. We prove that almost every simply connected polygon with at least four vertices has a simple spectrum. We also address the more general case of geodesic polygons in a constant curvature space form.References
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Additional Information
- Luc Hillairet
- Affiliation: Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629-Université de Nantes, 2 rue de la Houssinière, BP 92 208, F-44 322 Nantes Cedex 3, France
- MR Author ID: 705179
- Email: Luc.Hillairet@math.univ-nantes.fr
- Chris Judge
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47401
- MR Author ID: 349512
- Email: cjudge@indiana.edu
- Received by editor(s): September 4, 2007
- Received by editor(s) in revised form: April 22, 2008
- Published electronically: January 8, 2009
- Communicated by: Matthew J. Gursky
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2139-2145
- MSC (2000): Primary 58J50
- DOI: https://doi.org/10.1090/S0002-9939-09-09621-X
- MathSciNet review: 2480296