no. 4
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
1 Shizuoka University Department of Mathematics Ohya, Shizuoka 422-8529 (Japan)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1557-1572.

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.

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.

DOI : 10.5802/aif.2651
Classification : 58J50, 53C21
Keywords: Laplace-Beltrami operator, discrete spectrum, Ricci curvature
Mot 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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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2651/

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