In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston (1982), 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.
The ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume. When the manifold is compact or of finite volume, the Mostow rigidity theorem states that the fundamental group determines 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.
Minsky (2010) and Brock, Canary & Minsky (2012) proved the ending lamination conjecture for Kleinian surface groups. 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.
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geodesic laminations on some surfaces in the boundary of the manifold. The endinglaminationtheorem is a generalization of the Mostow rigidity theorem to hyperbolic...
hyperbolic 3-manifolds, together with the density theorem for Kleinian groups and the endinglaminationtheorem. It also implies the Ahlfors measure conjecture...
density conjecture was finally proved using the tameness theorem and the endinglaminationtheorem by Namazi & Souto (2012) and Ohshika (2011). Bers, Lipman...
American education strategy Kolb's experiential learning theory Endinglaminationtheorem Extremely large telescope, a type of telescope Extremely Large...
and James M. Henle, 2008) Tameness conjecture (Ian Agol, 2004) Endinglaminationtheorem (Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky, 2004) Carpenter's...
professor at Yale University. He is known for having proved Thurston's endinglamination conjecture and as a student of curve complex geometry. Minsky obtained...
resulted in a solution to the "EndingLamination Conjecture" of William Thurston, culminating in the geometric classification theorem for (topologically finite)...
his celebrated hyperbolic Dehn surgery theorem. To complete the picture, Thurston proved a hyperbolization theorem for Haken manifolds. A particularly important...
particularly motivating mathematical theorem. The change was prompted by a special case of the uniformization theorem, according to which, in his own words:...
adding measured foliations is essential in the definition of the endinglaminations of a hyperbolic 3-manifold. A point in Teichmüller space T ( S ) {\displaystyle...
30, 2013. Namazi, Hossein; Souto, Juan (2010), Non-realizability, endinglaminations and the density conjecture, archived from the original on July 15...
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