2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66554We give the first part of a proof of Thurston's Ending Lamination conjecture. In this part we show how to construct from the end invariants of a Kleinian surface group a ``Lipschitz model'' for the thick part of the corresponding hyperbolic manifold. This enables us to describe the topological structure of the thick part, and to give a-priori geometric bounds.102 pages, 13 figures. Slight revision of the statement of the main theorem, and a more complete discussion of the exterior of the convex coreGeometric TopologyDifferential Geometry30F40; 57M50text