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Problèmes de petites valeurs propres sur les surfaces de courbure moyenne constante
Author(s):
Philippe
Castillon
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1153-1163.
MSC (2000):
Primary 53C42, 53A10, 58J50;
Secondary 58J35
Posted:
October 12, 2001
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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:
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
Posted:
October 12, 2001
Communicated by:
Jozef Dodziuk
Copyright of article:
Copyright
2001,
American Mathematical Society
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