The spectrum of Kleininan manifolds

Details The spectrum of Kleininan manifolds The spectrum of Kleininan manifolds

1998-10-26

arxiv.org/abs/math/9810146v1

Mathematics

Differential Geometry

79 pages

Scientific paper

We obtain the Plancherel theorem for the quotient of a simple Lie group of real rank one by a convex-cocompact discrete subgroup and its consequences for the spectrum of locally invariant differential operators on bundles over Kleinian manifolds. We develop a geometric version of scattering theory. The paper is an update of dg-ga/9609011, which is completely rewritten from the point of view of representation theory. In particular, we are now able to show the meromorphy of Eisenstein series for all parameters.

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