Limits of limit sets I
Metric Geometry
2013-11-20 v1 Geometric Topology
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 of limit sets converge pointwise but not uniformly.
Cite
@article{arxiv.1107.0875,
title = {Limits of limit sets I},
author = {Mahan Mj and Caroline Series},
journal= {arXiv preprint arXiv:1107.0875},
year = {2013}
}
Comments
39 pages, 3 figures