Limits of limit sets I

Details Limits of limit sets I Limits of limit sets I

2011-07-05

arxiv.org/abs/1107.0875v1

Mathematics

Metric Geometry

39 pages, 3 figures

Scientific paper

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.

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