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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Philippe Castillon
Journal: Proc. Amer. Math. Soc. 130 (2002), 1153-1163
MSC (2000): Primary 53C42, 53A10, 58J50; Secondary 58J35
Published electronically: October 12, 2001
MathSciNet review: 1873791
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Abstract: 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.


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Additional Information

Philippe Castillon
Affiliation: Institut Fourier, B.P. 74, 38402 Saint Martin d’Hères Cedex, France
Address at time of publication: Département des Sciences Mathématiques, cc 51, Université Montpellier 2, 34 095 Montpellier cedex 5, France
Email: philippe.castillon@ujf-grenoble.fr, philippe.castillon@math.univ-montp2.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06295-5
PII: S 0002-9939(01)06295-5
Keywords: Surfaces de courbure moyenne constante, op\'erateur de stabilit\'e, th\'eorie spectrale
Received by editor(s): October 11, 2000
Published electronically: October 12, 2001
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2001 American Mathematical Society