On the essential spectrum of complete non-compact manifolds

Details On the essential spectrum of complete non-compact manifolds On the essential spectrum of complete non-compact manifolds

2010-03-12

arxiv.org/abs/1003.2502v2

Journal of Functional Analysis 260, (2011) 3283- 3298

Mathematics

Differential Geometry

Scientific paper

10.1016/j.jfa.2010.10.010

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.

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