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

@inproceedings{CANARY2003ApproximationBM,
  title={Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups},
  author={RICHARD D. CANARY and Marc Culler and Sa’ar Hersonsky and PETER B. SHALEN},
  year={2003}
}
  • RICHARD D. CANARY, Marc Culler, +1 author PETER B. SHALEN
  • Published 2003
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… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 36 references

On Thurston’s uniformization theorem for three-dimensional manifolds

  • J. W. Morgan
  • ‘The Smith Conjecture’, ed. by J. Morgan and H…
  • 1984
Highly Influential
4 Excerpts

On moduli of Kleinian groups

  • L. Bers
  • Russian Math Surveys 29
  • 1974
Highly Influential
10 Excerpts

The geometry of finitely generated Kleinian groups

  • A. Marden
  • Ann. of Math. 99
  • 1974
Highly Influential
8 Excerpts

Comparison of hyperbolic and extremal lengths

  • B. Maskit
  • Ann. Acad. Sci. Fenn. 10
  • 1985
Highly Influential
10 Excerpts

Shalen, Varieties of group representations and splittings of 3manifolds

  • P.B.M. Culler
  • Ann. of Math
  • 1983
Highly Influential
6 Excerpts

Grafting

  • H. Tanigawa
  • harmonic maps and projective structures on…
  • 1997
Highly Influential
2 Excerpts

Similar Papers

Loading similar papers…