The lower bound of the Ricci curvature that yields the infinite number of the discrete spectrum of the Laplacian

Hironori Kumura

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arXiv · 0902.1919

The lower bound of the Ricci curvature that yields the infinite number of the discrete spectrum of the Laplacian

Hironori Kumura

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Abstract

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.

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Hironori Kumura. 2009-02-11. The lower bound of the Ricci curvature that yields the infinite number of the discrete spectrum of the Laplacian. https://arxiv.org/abs/0902.1919

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