Perturbation of a warped product metric of an end and the growth property of solutions to eigenvalue equations

Abstract

On a Riemannian manifold, its geometric and analytic properties are crossly related with each other, and to study their relationship is an important subject. This paper studies the absence of eigenvalues, focusing on the curvatures near infinity; we first study rotationally symmetric cases, and, after that, investigate further possibilities, considering perturbations of rotationally symmetric metrics.