  In this paper, we classify completely hyperbolic 3-manifolds corresponding to
geometric limits of Kleinian surface groups isomorphic to $\pi_1(S)$ for a
finite-type hyperbolic surface $S$. In the first of the three main theorems, we
construct bi-Lipschitz model manifolds for such hyperbolic 3-manifolds, which
have a structure called brick decomposition and are embedded in $S \times
(0,1)$. In the second theorem, we show that conversely, any such model manifold
admitting a brick decomposition with reasonable conditions is bi-Lipschitz
homeomorphic to a hyperbolic manifold corresponding to some geometric limit of
quasi-Fuchsian groups. In the third theorem, it is shown that we can define end
invariants for hyperbolic 3-manifolds appearing as geometric limits of Kleinian
surface groups, and that the homeomorphism type and the end invariants
determine the isometric type of a manifold, which is analogous to the ending
lamination theorem for the case of finitely generated Kleinian groups. These
constitute an attempt to give an answer to the 8th question among the 24
questions raised by Thurston in his BAMS paper.
