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Moduli of continuity of Cannon-Thurston maps. (English) Zbl 1098.30032
Minsky, Yair (ed.) et al., Spaces of Kleinian groups. Proceedings of the programme ‘Spaces of Kleinian groups and hyperbolic 3-manifolds’, Cambridge, UK, July 21–August 15, 2003. Cambridge: Cambridge University Press (ISBN 0-521-61797-9/pbk). London Mathematical Society Lecture Note Series 329, 121-149 (2006).
Summary: We deal with the moduli of continuity of Cannon-Thurston maps for Kleinian 2-orbifold groups with bounded geometry. As an application, we establish the continuity of Cannon-Thurston maps when the corresponding representations vary. We also obtain an estimate for a fractal measure of a set of endpoints of leaves of a certain geodesic lamination.
For the entire collection see [Zbl 1089.30004].

30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
57M50 General geometric structures on low-dimensional manifolds
30C20 Conformal mappings of special domains