Asymptotic structures of non-compact hyperbolic 3-manifoIds and differential geometry

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We have been studying the topological properties of the deformation spaces of hyperbolic structures on 3-manifolds making use of differential geometry and low-dimensional manifold theory. In particular, we investigated the behavior of hyperbolic structures on the boundaries of quasi-conformal deformation spaces, which is known to coincide with the boundaries of the entire deformation spaces. As a result of this line of research, Ohshika proved that Bers-Thurston conjecture, which states that every finitely generated Kleinian group would be an algebraic limit of quasi-conformal deformations of a geometrically finite group, follows once Marden's tameness conjecture is proved to be true. This should be an important progress towards the solution of the ultimate problem of classifying the hyper-bolic structures on a given 3-manifold with finitely generated fundamental group.