On the essential spectrum of the Laplacian and vague convergence of the curvature at infinity

Hironori Kumura

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arXiv · math/0505523

On the essential spectrum of the Laplacian and vague convergence of the curvature at infinity

Hironori Kumura

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Abstract

We shall prove that under some volume growth condition, the essential spectrum of the Laplacian contains the interval $[(n-1)^2K/4, \infty)$ if an $n$-dimensional Riemannian manifold has an end and the average of the part of the Ricci curvature on the end which lies below a nonpositive constant $(n-1)K$ converges to zero at infinity.

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Hironori Kumura. 2005-05-25. On the essential spectrum of the Laplacian and vague convergence of the curvature at infinity. https://arxiv.org/abs/math/0505523

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