On P. J. Myrberg’s approximation theorem for some Kleinian groups

A Trace-class Rigidity Theorem for Kleinian Groups

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 th...

The limit set intersection theorem for finitely generated Kleinian groups

The proof of the Theorem proceeds by showing that it holds in some special cases involving Kleinian groups with connected limit sets, and then extending to the general case by using a decomposition argument based on the Klein-Maskit combination theorems and a careful tracking of the limit points resulting from this decomposition. We discuss various well-behaved classes of limit points in Sectio...

Commensurability riteria for Kleinian groups

Some Results on p-Best Approximation in Vector Spaces

Bounded Geometry for Kleinian Groups

We show that a Kleinian surface group, or hyperbolic 3manifold with a cusp-preserving homotopy-equivalence to a surface, has bounded geometry if and only if there is an upper bound on an associated collection of coefficients that depend only on its end invariants. Bounded geometry is a positive lower bound on the lengths of closed geodesics. When the surface is a once-punctured torus, the coeff...