11 citations · 30 across the 10 of their papers we have counts for
4 papers · 1 filter
Perturbation of a warped product metric of an end and the growth property of solutions to eigenvalue equation
Hironori Kumura
When a Riemannian manifold is rotationally symmetric, the critical order of the lower bound of radial curvatures for the absence of eigenvalues of the Laplacian is equal to…
The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II
Hironori Kumura
Under the quadratic-decay-conditions of the radial curvatures of an end, we shall derive growth estimates of solutions to the eigenvalue equation and show the absence of eigenvalue…
The lower bound of the Ricci curvature that yields the infinite number of the discrete spectrum of the Laplacian
Hironori Kumura
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 w…
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…