M. Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Nadirashvili N.
On the multiplicity of eigenvalues of the Laplacian on surfaces
(17K, LaTeX2e)

ABSTRACT.  We show that the multiplicity of the eigenvalues of the
Laplace Beltrami operator on compact Riemannian surfaces with
genus zero is bounded by $m(\lambda_k) \le 2k-3 $ for $k\ge3$.
Here we label the eigenvalues in the following way:
$0=\lambda_1<\lambda_2\le \lambda_3\dots$.