Quasiconvexity of Bands in Hyperbolic 3-Manifolds

Abstract

Abstract. Let M by a complete hyperbolic 3-manifold homotopy equivalent to a compact surface Σ. Let Φ be a proper subsurface of Σ, whose boundary is sufficiently short in M . We show that the union of all Margulis tubes and cusps homotopic into Φ lifts to a uniformly quasiconvex subset of hyperbolic 3-space.