## Journal of Differential Geometry

### Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups

#### Abstract

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.

#### Article information

Source
J. Differential Geom., Volume 64, Number 1 (2003), 57-109.

Dates
First available in Project Euclid: 21 July 2004

https://projecteuclid.org/euclid.jdg/1090426888

Digital Object Identifier
doi:10.4310/jdg/1090426888

Mathematical Reviews number (MathSciNet)
MR2015044

Zentralblatt MATH identifier
1069.57004

#### Citation

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