On a positivity preservation property for Schr\"odinger operators on   Riemannian manifolds
  We study a positivity preservation property for Schr\"odinger 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. 
Ognjen Milatovic
math.AP math.SP