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

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

2005-05-25

arxiv.org/abs/math/0505523v1

Mathematics

Differential Geometry

12 pages

Scientific paper

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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