Title

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

Document Type

Article

Publication Date

1-1-2021

Subject Area

ARRAY(0x5645c2cbe360)

Abstract

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.

Publication Title

Potential Analysis

Digital Object Identifier (DOI)

10.1007/s11118-020-09897-7

ISSN

09262601

E-ISSN

1572929X

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