Limits of limit sets I
- First Online:
- Cite this article as:
- Mj, M. & Series, C. Geom Dedicata (2013) 167: 35. doi:10.1007/s10711-012-9803-4
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.
KeywordsKleinian group Limit set Geometrically finite Cannon–Thurston map
Mathematics Subject Classification (2010)30F40 57M50
Unable to display preview. Download preview PDF.