On m-Accretivity of Perturbed Bochner Laplacian in L ^p Spaces on Riemannian Manifolds

Abstract

We consider a differential expression ${H=\nabla^*\nabla+V}$, where ${\nabla}$ is a Hermitian connection on a Hermitian vector bundle E over a manifold of bounded geometry (M, g) with metric g, and V is a locally integrable section of the bundle of endomorphisms of E. We give a sufficient condition for H to have an m-accretive realization in the space L ^p(E), where 1 < p <  +∞. We study the same problem for the operator Δ _M  + V in L ^p(M), where 1 < p < ∞, Δ _M is the scalar Laplacian on a complete Riemannian manifold M, and V is a locally integrable function on M.