The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian
Annales de l'Institut Fourier, Volume 61 (2011) no. 4, pp. 1557-1572.

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
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, Volume 61 (2011) no. 4, pp. 1557-1572. doi : 10.5802/aif.2651. http://archive.numdam.org/articles/10.5802/aif.2651/

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