Operator $\hat{I}”-aS$ on warped product manifolds

Abstract

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