Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds
Analysis of PDEs
2009-06-12 v1 Differential Geometry
Abstract
In this paper, we establish sharp inequalities for four kinds of classical eigenvalues on a bounded domain of a Riemannian manifold. We also establish asymptotic formulas for the eigenvalues of the buckling and clamped plate problems. In addition, we give a negative answer to the Payne conjecture for the one-dimensional case.
Cite
@article{arxiv.0906.2043,
title = {Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds},
author = {Genqian Liu},
journal= {arXiv preprint arXiv:0906.2043},
year = {2009}
}