Geodesic
The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian
[Limite inférieure de la courbure de Ricci qui donne un nombre de spectre discret infini]
Kumura, Hironori1
1Shizuoka University Department of Mathematics Ohya, Shizuoka 422-8529 (Japan)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1557-1572
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This paper discusses the question whether the discrete spectrum of the Laplace-Beltrami operator is infinite or finite. The borderline-behavior of the curvatures for this problem will be completely determined.

Ce document traite de la question si le spectre discret de l’opérateur de Laplace-Beltrami est infini ou fini. La ligne de démarcation du comportement des courbures de ce problème sera complètement déterminée.

DOI : 10.5802/aif.2651
Classification : 58J50, 53C21
Keywords: Laplace-Beltrami operator, discrete spectrum, Ricci curvature
Mots-clés : opérateur de Laplace-Beltrami, spectre discret, courbure de Ricci

Kumura, Hironori  1

1 Shizuoka University Department of Mathematics Ohya, Shizuoka 422-8529 (Japan) 
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     title = {The lower bound of the {Ricci} curvature that yields an infinite discrete spectrum of the {Laplacian}},
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Kumura, Hironori. The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1557-1572. doi: 10.5802/aif.2651

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