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Kleinian groups, Laplacian on forms and currents at infinity

Author: Mark Pollicott
Journal: Proc. Amer. Math. Soc. 110 (1990), 269-279
MSC: Primary 58G25; Secondary 22E40, 30F40, 58F17, 58F20
MathSciNet review: 1012936
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Abstract: In this note we consider the spectrum of the Laplacian acting on the space of (co-closed) differential forms on the quotient of $ n$-dimensional hyperbolic space by a co-compact Kleinian group. Using a result of P.-Y. Gaillard we relate these to currents on the sphere at infinity of hyperbolic space with distinctive transformation properties under the action of the group. We analyse these currents using zeta-functions and Ruelle's Transfer operator. This represents a partial extension of earlier work of the author related to Fuchsian groups. In an appendix we propose an alternative approach to related questions.

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Keywords: Kleinian groups, Laplacian, differential forms, transfer operator, zeta function, limit set
Article copyright: © Copyright 1990 American Mathematical Society

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