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This paper deals with the spectra of the Laplace and stability operators of a constant mean curvature surface in the hyperbolic space. In a preceding work, the author described the essential spectra of these operators, assuming that the surface is of finite total curvature. In this paper, we prove that these two operators have a finite number of eigenvalues below their essential spectra.

Problèmes de petites valeurs propres sur les surfaces de courbure moyenne constante