In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston (1982) as the eleventh problem out of his twenty-four questions, states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in the boundary of the manifold.
When the volume is infinite the fundamental group is not enough to determine the manifold: one also needs to know the hyperbolic structure on the surfaces at the "ends" of the manifold, and also the ending laminations on these surfaces.
In view of the Tameness theorem this implies the ending lamination conjecture for all finitely generated Kleinian groups, from which the general case of ELT follows.
The ending lamination of this end is (roughly) a lamination on the surface S, in other words a closed subset of S that is written as the disjoint union of geodesics of S. It is characterized by the following property.
Suppose that there is a sequence of closed geodesics on S whose lifts tends to infinity in the end.