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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generic spectral simplicity of polygons


Authors: Luc Hillairet and Chris Judge
Journal: Proc. Amer. Math. Soc. 137 (2009), 2139-2145
MSC (2000): Primary 58J50
Published electronically: January 8, 2009
MathSciNet review: 2480296
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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.


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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
Email: Luc.Hillairet@math.univ-nantes.fr

Chris Judge
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47401
Email: cjudge@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09621-X
PII: S 0002-9939(09)09621-X
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
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.