98-126 M. Hoffmann-Ostenhof M., Hoffmann-Ostenhof T., Nadirashvili N.

On the multiplicity of eigenvalues of the Laplacian on surfaces (17K, LaTeX2e) Mar 4, 98

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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: $0=\lambda_1<\lambda_2\le \lambda_3\dots$.

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