Volume 21, issue 2 (2017)

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Limits of limit sets, II: Geometrically infinite groups

Mahan Mj and Caroline Series

Geometry & Topology 21 (2017) 647–692

We show that for a strongly convergent sequence of purely loxodromic finitely generated Kleinian groups with incompressible ends, Cannon–Thurston maps, viewed as maps from a fixed base limit set to the Riemann sphere, converge uniformly. For algebraically convergent sequences, we show that there exist examples where even pointwise convergence of Cannon–Thurston maps fails.

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Kleinian group, limit set, Cannon–Thurston map, geometrically infinite group
Mathematical Subject Classification 2010
Primary: 30F40, 57M50
Received: 13 June 2013
Revised: 7 June 2015
Accepted: 20 May 2016
Published: 17 March 2017
Proposed: Jean-Pierre Otal
Seconded: Bruce Kleiner, Martin Bridson
Mahan Mj
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400005
Caroline Series
Mathematics Institute
University of Warwick
United Kingdom