2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70596Given a compact orientable 3-manifold M whose boundary is a hyperbolic surface and a simple closed curve C in its boundary, every knot in M is homotopic to one whose complement admits a complete hyperbolic structure with totally geodesic boundary in which the geodesic representative of C is as small as you like.10 pages, no figures, the exposition has been polished, typographical errors corrected, a modicum of detail added, to appear in Proceedings of the AMSGeometric Topology57M50text