Open Access
2017 Limits of limit sets, II: Geometrically infinite groups
Mahan Mj, Caroline Series
Geom. Topol. 21(2): 647-692 (2017). DOI: 10.2140/gt.2017.21.647

Abstract

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.

Citation

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Mahan Mj. Caroline Series. "Limits of limit sets, II: Geometrically infinite groups." Geom. Topol. 21 (2) 647 - 692, 2017. https://doi.org/10.2140/gt.2017.21.647

Information

Received: 13 June 2013; Revised: 7 June 2015; Accepted: 20 May 2016; Published: 2017
First available in Project Euclid: 16 November 2017

MathSciNet: MR3626590
zbMATH: 1369.30045
Digital Object Identifier: 10.2140/gt.2017.21.647

Subjects:
Primary: 30F40 , 57M50

Keywords: Cannon–Thurston map , geometrically infinite group , Kleinian group , limit set

Rights: Copyright © 2017 Mathematical Sciences Publishers

Vol.21 • No. 2 • 2017
MSP
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