Essential Self-Adjointness of Perturbed Biharmonic Operators via Conformally Transformed Metrics

We give sufficient conditions for the essential self-adjointness of perturbed biharmonic operators acting on sections a Hermitian vector bundle over Riemannian manifold with additional assumptions, such as lower semi-bounded Ricci curvature or bounded sectional curvature. In case curvature, we formulate our results in terms completeness metric that is conformal to original one, via factor depends minorant perturbing potential V. situation, are able relax growth condition V imposed an earlier article. this context, consistent literature $\mathbb {R}^{n}$ .