Estimates of eigenvalues of a clamped problem

Abstract

In this paper, for the eigenvalue problem of a clamped plate problem on complex projective space with holomorphic sectional curvature c(> 0) and n(≥ 3)-dimensional noncompact simply connected complete Riemannian manifold with sectional curvature Sec satisfying − a ² ≤ Sec ≤ − b ², where a ≥ b ≥ 0 are constants, we obtain universal eigenvalue inequalities. Moreover, we deduce the estimates of the upper bounds of eigenvalues.