Operator $\Delta-aS$ on warped product manifolds

TL;DR

This paper investigates the stability properties of a family of differential operators involving the Laplacian and scalar curvature on warped product manifolds, extending understanding of geometric analysis in such settings.

Contribution

It introduces a detailed analysis of the operator $L_a= riangle - aS$ on warped product manifolds, focusing on stability criteria and spectral properties.

Findings

Characterization of stability conditions for $L_a$

Spectral analysis of $L_a$ on warped products

Insights into geometric analysis of warped manifolds

Abstract

In this work we studied the stability of the family of operators $L_a=\Delta-aS$, $a\in\mathbb R$, in a warped product of an infinite interval or real line by one compact manifold, where $\Delta$ is the Laplacian and $S$ is the scalar curvature of the resulting manifold.