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arXiv:math/9801090 [math.AP]AbstractReferencesReviewsResources

Bounds on the multiplicity of eigenvalues for fixed membranes

Thomas Hoffman-Ostenhof, Peter W. Michor, Nikolai Nadirashvili

Published 1998-01-20, updated 1999-06-02Version 3

For a membrane in the plane the multiplicity of the $k$-th eigenvalue is known to be not greater than $2k-1$. Here we prove that it is actually not greater than $2k-3$, for $k\ge 3$.

Comments: AmSTeX, epsf.tex, 17 encapsulated postscript figures, 17 pages. Third version with minor stylistic improvements
Journal: Geometric And Functional Analysis (GAFA). Vol. 9 (1999), 1169-1188
Categories: math.AP, math.DG
Subjects: 35B05, 35P15, 58G25
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