05-2 Jochen Bruening, Vladimir Geyler

Geometric Scattering on Compact Riemannian Manifolds and Spectral Theory of Automorphic Functions (23K, AMS-TeX) Jan 5, 05

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Abstract. We show that the spectral properties of the Laplace--Beltrami operator on a compact Riemannian manifold with $n$ semi-lines attached to it are similar to those for a finite-volume hyperbolic manifold with $n$ cusps. Our results are further justification of the Gromov--Novikov thesis concerning relations between Hyperbolic Geometry on infinity and One-Dimensional Geometry. As an application of the corresponding results we obtain a relation between the scattering matrix on a compact Riemann surface of constant negative curvature and the Selberg zeta function for this surface.

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