Bounds on the multiplicity of eigenvalues for fixed membranes

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

Bounds on the multiplicity of eigenvalues for fixed membranes

Authors

Hoffman-Ostenhof, Thomas

Michor, Peter W.

Nadirashvili, Nikolai

Description

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 $k\ge 3$.
AmSTeX, epsf.tex, 17 encapsulated postscript figures, 17 pages. Third version with minor stylistic improvements