QUASICONVEXITY OF BANDS IN HYPERBOLIC 3-MANIFOLDS.

Let $M$ be a complete hyperbolic 3-manifold homotopy equivalent to a compact surface $\Sigma $. Let $\Phi $ be a proper subsurface of $\Sigma $, whose boundary is sufficiently short in $M$. We show that the union of all Margulis tubes and cusps homotopic into $\Phi $ lifts to a uniformly quasiconvex subset of hyperbolic 3-space. [ABSTRACT FROM AUTHOR]