@Article{JPDE-5-87,
author = {Li Jiayu},
title = {The Problem of Eigenvalue on Noncompact Complete Riemannian Manifold},
journal = {Journal of Partial Differential Equations},
year = {1992},
volume = {5},
number = {4},
pages = {87--95},
abstract = { Let M be an n-dimensional noncompact complete Riemannian manifold, "&#916" is the Laplacian of M. It is a negative selfadjoint operator in L&sup2(M). First, we give a criterion of non-existence of eigenvalue by the heat kernel. Applying the criterion yields that the Laplacian on noncompact constant curvature space form has no eigenvalue. Then, we give a geometric condition of M under which the Laplacian of M has eigenvalues. It implies that changing the metric on a compact domain of constant negative curvature space form may yield eigenvalues.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5756.html}
}