Eigenvalue estimates on domains in complete noncompact Riemannian manifolds
Daguang Chen, Tao Zheng, Lu Min · Pacific Journal of Mathematics · 2012
In this paper, we obtain universal inequalities for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian and the clamped plate problem on a bounded domain in an n-dimensional (n ≥ 3) noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying -K 2 ≤ Sec ≤ -k 2 , where K ≥ k ≥ 0 are constants.When M is ވ n (-1) (n ≥ 3), these inequalities become ones previously found by Cheng and Yang.