On the essential spectrum of complete non-compact manifolds

Abstract

In this paper, we prove that the L p essential spectra of the Laplacian on functions are [ 0 , + ∞ ) on a non-compact complete Riemannian manifold with non-negative Ricci curvature at infinity. The similar method applies to gradient shrinking Ricci soliton, which is similar to non-compact manifold with non-negative Ricci curvature in many ways.