On a positivity preservation property for Schrödinger operators on Riemannian manifolds

Abstract

We study a positivity preservation property for Schrödinger operators with singular potential on geodesically complete Riemannian manifolds with non-negative Ricci curvature. We apply this property to the question of self-adjointness of the maximal realization of the corresponding operator.

We updated some information in the bibliography. The final version of this preprint will appear in Proceedings of the American Mathematical Society