The Hausdorff dimension of non-conical and Myrberg limit sets equals the critical exponent in several negatively curved settings, confirming the Falk-Matsuzaki conjecture.
The classification of Kleinian surface groups, II: The Ending Lamination Conjecture
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abstract
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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Hausdorff Dimension of non-conical and Myrberg limit sets
The Hausdorff dimension of non-conical and Myrberg limit sets equals the critical exponent in several negatively curved settings, confirming the Falk-Matsuzaki conjecture.