Limiting absorption principle on manifolds having ends with various measure growth rate limits

Details Limiting absorption principle on manifolds having ends with various measure growth rate limits Limiting absorption principle on manifolds having ends with various measure growth rate limits

2006-06-06

arxiv.org/abs/math/0606125v12

Mathematics

Differential Geometry

32 page

Scientific paper

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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