11 citations · 30 across the 10 of their papers we have counts for
10 papers
Uniqueness of solutions, radiation conditions, and complexity of the metric at infinity
Hironori Kumura
The purpose of this paper is to prove the uniqueness theorem of solutions of eigenvalue equations on one end of Riemannian manifolds for drift Laplacians, including the standard La…
Positive and negative growth rates of measures and pointwise bounds of solutions of eigenvalue equations
Hironori Kumura
This paper, focusing on the growth rate of the measure, gives pointwise bounds of solutions of eigenvalue equations of the Laplace-Beltrami operator on noncompact Riemannian manifo…
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…
Infimum of the exponential volume growth and the bottom of the essential spectrum of the Laplacian
Hironori Kumura
The purpose of this paper is to point out that `supremum' in two inequalities of Brooks should be replaced with `infimum'. The results of this paper are already known by Professor…
Limiting absorption principle on manifolds having ends with various measure growth rate limits
Hironori Kumura
The purpose of this paper is to study the property of the resolvent of the Laplace-Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which ha…
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…
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…