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 $[0,+\infty )$ 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.

Minor modifications

References in corpus (1)

• Recent Progress on Ricci Solitons

Cited by in corpus (9)

• Location of the essential spectrum in curved quantum layers
• Eigenvalues of the drifted Laplacian on complete metric measure spaces
• Density and spectrum of minimal submanifolds in space forms
• Compact submanifolds supporting singular interactions
• The spectrum of the Laplacian on forms
• Heat kernel estimates and the essential spectrum on weighted manifolds
• Ancient mean curvature flows from minimal hypersurfaces
• Spectrum of the Laplacian on radial graphs
• Essential spectrum of a class of Riemannian manifolds