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math.DG2009★ 1 cited
The uncertainty principle lemma under gravity and the discrete spectrum of Schrödinger operators
Kazuo Akutagawa, Hironori Kumura
The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schrödinger operator has…
math.DG2005
On the essential spectrum of the Laplacian and vague convergence of the curvature at infinity
Hironori Kumura
We shall prove that under some volume growth condition, the essential spectrum of the Laplacian contains the interval if an -dimensional Riemannian manifo…
math.DG2005
The radial curvature of an end that makes eigenvalues vanish in the essential spectrum I
Hironori Kumura
The concern of this paper is to clarify a relationship between the curvatures at infinity and the spectral structure of the Laplacian. In particular, this paper discusses the quest…