The L^p Positivity preservation on Riemannian manifolds

In his investigations on the spectral theory of Schrödinger operators with singular potentials, T. Kato introduced many celebrated tools and a lot of work has been done to transplant them to Riemannian manifolds. In this talk I shall mainly focus on the so called “L^p Positivity Preservation” and discuss how it is (un)related to the geometry of the underlying space.
The talk is based on a joint work with Daniele Valtorta and Giona Veronelli