Estimates for eigenvalues of the Paneitz operator

TL;DR

This paper derives sharp estimates for the eigenvalues of the Paneitz operator on compact submanifolds in Euclidean space, contributing to spectral geometry understanding.

Contribution

It provides the first sharp eigenvalue estimates for the Paneitz operator on submanifolds, extending spectral analysis in geometric analysis.

Findings

Eigenvalue estimates are sharp.

Results apply to n-dimensional submanifolds in Euclidean space.

Advances spectral geometry of the Paneitz operator.

Abstract

For an $n$-dimensional compact submanifold $M^n$ in the Euclidean space $\mathbf R^{N}$, we study estimates for eigenvalues of the Paneitz operator on $M^n$. Our estimates for eigenvalues are sharp.