On the essential spectrum of complete non-compact manifolds

Zhiqin Lu; Detang Zhou

doi:10.1016/j.jfa.2010.10.010

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arXiv · 1003.2502

On the essential spectrum of complete non-compact manifolds

Zhiqin Lu·Detang Zhou

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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.

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BibTeX RIS

Zhiqin Lu, Detang Zhou. 2014-01-07. On the essential spectrum of complete non-compact manifolds. https://doi.org/10.1016/j.jfa.2010.10.010

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