Journal of Differential Geometry
- J. Differential Geom.
- Volume 64, Number 1 (2003), 57-109.
Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups
Let M be a compact, oriented, irreducible, atoroidal 3-manifold with nonempty boundary. Let CC0(M) denote the space of convex cocompact Kleinian groups uniformizing M. We show that any Kleinian group in the boundary of CC0(M) whose limit set is the whole sphere can be approximated by maximal cusps. Density of maximal cusps on the boundary of Schottky space is derived as a corollary. We further show that maximal cusps are dense in the boundary of the quasiconformal deformation space of any geometrically finite hyperbolic 3-manifold with connected conformal boundary.
J. Differential Geom., Volume 64, Number 1 (2003), 57-109.
First available in Project Euclid: 21 July 2004
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Canary, Richard D.; Culler, Marc; Hersonsky, SA'AR; Shalen, Peter B. Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups. J. Differential Geom. 64 (2003), no. 1, 57--109. doi:10.4310/jdg/1090426888. https://projecteuclid.org/euclid.jdg/1090426888