On m-accretive Schrödinger operators in [formula omitted]-spaces on manifolds of bounded geometry

Abstract

Let ( M , g ) be a manifold of bounded geometry with metric g. We consider a Schrödinger-type differential expression H = Δ M + V , where Δ M is the scalar Laplacian on M and V is a nonnegative locally integrable function on M. We give a sufficient condition for H to have an m-accretive realization in the space L p ( M ) , where 1 < p < + ∞ . The proof uses Kato's inequality and L p -theory of elliptic operators on Riemannian manifolds.