Geometriae Dedicata

, Volume 167, Issue 1, pp 35–67

Limits of limit sets I

Original Paper

DOI: 10.1007/s10711-012-9803-4

Cite this article as:
Mj, M. & Series, C. Geom Dedicata (2013) 167: 35. doi:10.1007/s10711-012-9803-4
  • 178 Downloads

Abstract

We show that for a strongly convergent sequence of geometrically finite Kleinian groups with geometrically finite limit, the Cannon–Thurston maps of limit sets converge uniformly. If however the algebraic and geometric limits differ, as in the well known examples due to Kerckhoff and Thurston, then provided the geometric limit is geometrically finite, the maps on limit sets converge pointwise but not uniformly.

Keywords

Kleinian group Limit set Geometrically finite Cannon–Thurston map 

Mathematics Subject Classification (2010)

30F40 57M50 

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.School of Mathematical SciencesRKM Vivekananda UniversityDt. HowrahIndia
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK