Hoffmann-Ostenhof T., Michor P. W., Nadirashvili N.
Bounds on the Multiplicity of Eigenvalues for Fixed Membranes
(582K, Postscript)

ABSTRACT.  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 $k\ge3$.