6,207 research outputs found
Analytic torsion of complete hyperbolic manifolds of finite volume
In this paper we define the analytic torsion for a complete oriented
hyperbolic manifold of finite volume. It depends on a representation of the
fundamental group. For manifolds of odd dimension, we study the asymptotic
behavior of the analytic torsion with respect to certain sequences of
representations obtained by restriction of irreducible representations of the
group of isometries of the hyperbolic space to the fundamental group.Comment: 56 page
Scattering theory for the Laplacian on manifolds with bounded curvature
In this paper we study the behaviour of the continuous spectrum of the
Laplacian on a complete Riemannian manifold of bounded curvature under
perturbations of the metric. The perturbations that we consider are such that
its covariant derivatives up to some order decay with some rate in the geodesic
distance from a fixed point. Especially we impose no conditions on the
injectivity radius. One of the main results are conditions on the rate of
decay, depending on geometric properties of the underlying manifold, that
guarantee the existence and completeness of the wave operators.Comment: 45 page
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