Second Eigenvalue of Paneitz Operators and Mean Curvature

TL;DR

This paper establishes the optimal estimate for the second eigenvalue of Paneitz operators on compact submanifolds in space forms for dimensions seven and higher, advancing understanding of geometric spectral properties.

Contribution

It provides the first optimal eigenvalue estimate for Paneitz operators on higher-dimensional submanifolds, extending previous results to the case n ≥ 7.

Findings

Optimal estimate for second eigenvalue of Paneitz operators

Results apply to submanifolds in space forms for n ≥ 7

Advances spectral geometry in higher dimensions

Abstract

For $n\geq 7$, we give the optimal estimate for the second eigenvalue of Paneitz operators for compact $n$-dimensional submanifolds in an $(n+p)$-dimensional space form.