Geometric Finiteness and the Convergence of Kleinian Groups

Communications in Analysis and Geometry

Volumn 5, Issue 3, 1997, Pages 497-533

  Taylor, Edward C ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037511013     PISSN: 10198385     EISSN: None     Source Type: Journal    
DOI: 10.4310/CAG.1997.v5.n3.a5     Document Type: Article

References (43)

1. B. Abikoff, "On Boundaries of Teichmüller spaces and on Kleinian groups, III" Acta Math. 134(1975), pp. 211-237.
2. A.F. Beardon, The Geometry of Discrete Groups, Springer-Verlag, 1983.
3. R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry, Springer-Verlag, 1992.
4. L. Bers, "On boundaries of Teichmüller spaces and on Kleinian groups," Ann. of Math. (2) 91(1970), pp. 570-600.
5. L. Bers, "On moduli of Kleinian groups," Russian Math Surveys, 29(1974), pp. 88-102.
6. C. Bishop and P. Jones, "Hausdorff dimension and Kleinian groups", preprint.
7. F. Bonahon, "Bouts des variétés hyperboliques de dimension 3," Ann. of Math. 124(1986), pp. 71-158.
8. B.H. Bowditch, "Geometrical finiteness for hyperbolic groups," J. Funct. Anal. 113(1993), pp. 245-317.
9. B.H. Bowditch, "Some results on the geometry of convex hulls in manifolds of pinched negative curvature," Comment Math. Helv. 69(1994), pp. 49-81.
10. R. Brooks and J.P. Matelski, "Collars in Kleinian groups," Duke Math. J. 49(1982), pp. 163-182.
11. R. Canary, D.B.A. Epstein and P. Green, "Notes on notes of Thurston," in Analytical and Geometrical Aspects of Hyperbolic Spaces, Cambridge University Press, 1987, pp. 3-92.
12. R. Canary, "A covering theorem for hyperbolic 3-manifolds and its applications," Topology 35(1996), pp. 751-778.
13. R. Canary and Y. Minsky, "On limits of tame hyperbolic 3-manifolds," J. Differential Geom. 43(1996), pp. 1-41.
14. R. Canary, Y. Minsky and E. Taylor, "Spectral theory, Hausdorff dimension and the topology of hyperbolic 3-manifolds," J. Geom. Anal., to appear.
15. A Douady and C. Earle, "Conformally natural extensions of homeomorphisms of the circle," Acta Math. 157(1986), pp. 23-48.
16. C. Earle and A. Marden, "Quasifuchsian space and geometric complex coordinates for Teichmüller and moduli space," preprint.
17. D.B.A. Epstein et al., Word Processing in Groups, Jones and Bartlett, 1992.
18. D.B.A. Epstein and A. Marden, "Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces," in Analytical and Geometrical Aspects of Hyperbolic Spaces, Cambridge University Press, 1987, pp. 114-253.
19. K.J. Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1985.
20. F. Gehring and J. Väisälä, "Hausdorff dimension and quasi-conformal mappings," J. London Math. Soc. (2) 6(1973) pp. 504-512.
21. L. Greenberg, "Fundamental polyhedron for Kleinian groups," Ann. of Math. 84(1966), pp. 433-441.
22. T. Jørgensen, "On cyclic groups of Möbius transformations," Math. Scand. 33(1973), pp. 250-260.
23. T. Jørgensen, "On discrete groups of Möbius transformations," Amer. J. Math. 98(1976), pp. 739-749.
24. T. Jørgensen and A. Marden, "Algebraic and geometric convergence of Kleinian groups," Math. Scand. 66(1990), pp. 47-72.
25. L. Keen, B. Maskit and C. Series, "Geometric finiteness and uniqueness for Kleinian groups with circle packing limit sets," J. reine angew. Math. 436(1993), pp. 209-219.
26. S. Kerckhoff and W. Thurston, "Non-continuity of the modular group at Bers' boundary of Teichüller space," Invent. Math. 100 (1990), pp. 25-47.
27. A. Marden, "The geometry of finitely generated Kleinian groups," Ann. of Math. 99(1974), pp. 383-462.
28. A. Marden, "Geometric relations between homeomorphic Riemann surfaces," Bull. A.M.S. 3(1980), pp. 1001-1017.
29. A. Marden, personal communication at Gehring Conference, 1995.
30. G.A. Margulis, "Arithmeticity of nonuniform lattices," Funkcional Anal. Prilžen. 7(1973), pp. 88-89.
31. B. Maskit, "On boundaries of Teichmüller spaces and on Kleinian groups," Ann. of Math. 91(1970), pp. 607-639.
32. B. Maskit, Kleinian Groups, Springer-Verlag, 1988.
33. C. McMullen, "Cusps are dense," Ann. of Math. 133(1991), pp. 217-247.
34. J. Morgan, "Uniformization theorem for three-dimensional manifolds," in The Smith Conjecture, Academic Press, 1984, pp. 37-125.
35. G.D. Mostow, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes. Études Sci. Publ. Math. 34(1968), pp. 53-104.
36. H.M. Reimann, "Invariant extension of quasi-conformal deformations," Ann. Acad. Sci. Fenn. Ser. A I Math., 20 (1985), pp. 477-492.
37. P. Scott, "Compact submanifolds of 3-manifolds," J. London Math. Soc. 7(1973), pp. 246-250.
38. D. Sullivan, "A finiteness theorem for cusps," Acta Math. 147(1981), pp. 289-299.
39. D. Sullivan, "Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups," Acta Math. 153 (1984), pp. 259-277.
40. D. Sullivan, "Related aspects of positivity in Riemannian geometry," J. Differential Geom. 25(1987), pp. 327-351.
41. E.G. Taylor, "Spectral theory and the convergence of Kleinian groups," preprint.
42. W. Thurston, The Geometry and Topology of 3-manifolds, Lecture Notes, Department of Mathematics, Princeton University, Princeton 1979.
43. P. Tukia, "The Hausdorff dimension of the limit set of a geometrically finite Kleinian group," Acta Math. 152(1984), pp. 127-180.