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 of a Hermitian vector bundle over a Riemannian manifold with additional assumptions, such as lower semi-bounded Ricci curvature or bounded sectional curvature. In the case of lower semi-bounded Ricci curvature, we formulate our results in terms of the completeness of the metric that is conformal to the original one, via a conformal factor that depends on a minorant of the perturbing potential V. In the bounded sectional curvature situation, we are able to relax the growth condition on the minorant of V imposed in an earlier article. In this context, our growth condition on the minorant of V is consistent with the literature on the self-adjointness of perturbed biharmonic operators on ℝn.
Digital Object Identifier (DOI)
Milatovic, O., Saratchandran, H. Essential Self-Adjointness of Perturbed Biharmonic Operators via Conformally Transformed Metrics. Potential Anal 56, 623–647 (2022). https://doi.org/10.1007/s11118-020-09897-7