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

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

2009-02-11

arxiv.org/abs/0902.1919v7

Mathematics

Differential Geometry

8 pages; add some contexts in Introduction for readers, typos; typos, again; modified Abstract; Main theorem is generalized in

Scientific paper

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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