A Trace-class Rigidity Theorem for Kleinian Groups
نویسنده
چکیده
Suppose that ? 1 and ? 2 are geometrically nite, convex co-compact, discrete groups of isometries of real hyperbolic space H 3 whose domains of discontinuity are diieomorphic. We show that if the respective scattering matrices S 1 (s) and S 2 (s) diier from each other by a trace-class perturbation on the unitary axis Re(s) = 1, then ? 1 and ? 2 are conjugate in PSL(2; C). This result reeects the rigidity of hyperbolic three-manifolds.
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تاریخ انتشار 1995