Limiting absorption principle on manifolds having ends with various measure growth rate limits
Differential Geometry
2014-02-26 v9 Spectral Theory
Abstract
The purpose of this paper is to study the property of the resolvent of the Laplace-Beltrami operator on a noncompact complete Riemannian manifold with various ends each of which has a different limit of the growth rate of the Riemannian measure at infinity, in particular, focusing on the limiting absorption principle. As a result, we will obtain the absolute continuity of the Laplace-Beltrami operator.
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Cite
@article{arxiv.math/0606125,
title = {Limiting absorption principle on manifolds having ends with various measure growth rate limits},
author = {Hironori Kumura},
journal= {arXiv preprint arXiv:math/0606125},
year = {2014}
}
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32 page