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Generic spectral simplicity of polygons
Author(s):
Luc
Hillairet;
Chris
Judge
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2139-2145.
MSC (2000):
Primary 58J50
Posted:
January 8, 2009
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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.
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
Email:
Luc.Hillairet@math.univ-nantes.fr
Chris
Judge
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47401
Email:
cjudge@indiana.edu
DOI:
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
Posted:
January 8, 2009
Communicated by:
Matthew J. Gursky
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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