Let M by a complete hyperbolic 3-manifold homotopy equivaent to a compact surface Sigma. Let Phi be a subsurface of Sigma, whose boundary is sufficiently short in M. We show that the union of all Margulis tubes homotopic into Phi lifts to a uniformly quasiconvex subset of hyperbolic 3-space.
J. Austral. Math. Soc. 96 (2014) 167--185.