A rigidity theorem for discrete 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...

A Bowen type rigidity theorem for non-cocompact hyperbolic groups

We establish a Bowen type rigidity theorem for geometrically finite actions of the fundamental group of finite volume noncompact hyperbolic manifolds (with dimension at least 3). Mathematics Subject Classification (2000). 53C24, 30F40, 37F30.

A Rigidity Theorem for the Solvable Baumslag-solitar Groups

Local rigidity of discrete groups acting on complex hyperbolic space

The superrigidity theorem of Margulis, see Zimmer [17], classifies finite dimensional representations of lattices in semi-simple Lie groups of real rank strictly larger than 1. It is a fundamental problem to obtain the classification of finite dimensional representations of lattices in rank I semi-simple Lie groups. That this problem will be considerably harder than the previous one is suggeste...

A Rigidity Theorem for Convex Surfaces

Theorem 1. Let (S2, g) be the two dimensional sphere with a metric of class C1,1 whose Gaussian curvature satisfies 0 ≤ K ≤ 1. Then any simple closed geodesic γ on (S2, g) has length at least 2π. If the length of γ is 2π, then (S2, g) is isometric to the standard round sphere (S2, g0) and γ is a great circle on (S2, g0) or (S 2, g) is isometric to a circular cylinder of circumference 2π capped ...