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The classification of Kleinian surface groups, II: The Ending Lamination Conjecture

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arxiv math/0412006 v2 pith:LT6C7JT6 submitted 2004-12-01 math.GT math.DG

Jeffrey F. Brock , Richard D. Canary , Yair N. Minsky This is my paper · ORCID
classification math.GTmath.DG
keywords conjectureendingkleinianlaminationsurfacegeneralgroupgroups
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Thurston's Ending Lamination Conjecture states that a hyperbolic 3-manifold N with finitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this paper we prove this conjecture for Kleinian surface groups; the general case when N has incompressible ends relative to its cusps follows readily. The main ingredient is the establishment of a uniformly bilipschitz model for a Kleinian surface group. The first half of the proof appeared in math.GT/0302208, and a subsequent paper will establish the Ending Lamination Conjecture in general.

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  1. Hausdorff Dimension of non-conical and Myrberg limit sets

    math.GR 2025-06 conditional novelty 8.0 of 10

    The Hausdorff dimension of non-conical and Myrberg limit sets equals the critical exponent in several negatively curved settings, confirming the Falk-Matsuzaki conjecture.

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