Estimates for lower order eigenvalues of a clamped plate problem

TL;DR

This paper derives sharp, universal inequalities for the lower order eigenvalues of the clamped plate problem on bounded domains within Riemannian manifolds, advancing spectral geometry understanding.

Contribution

It provides new sharp, universal bounds for lower eigenvalues of the clamped plate problem on Riemannian manifolds, extending previous results.

Findings

Established sharp inequalities for eigenvalues

Universal bounds applicable to various domains

Enhanced understanding of spectral properties in Riemannian geometry

Abstract

For a bounded domain $\Omega$ in a complete Riemannian manifold $M^n$, we study estimates for lower order eigenvalues of a clamped plate problem. We obtain universal inequalities for lower order eigenvalues. We would like to remark that our results are sharp.