On isomorphisms of geometrically finite Möbius groups

 Access to full text

 Full (PDF)

1. [1] L. V. AHLFORS, Fundamental polyhedrons and limit point sets of Kleinian groups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 251-254. Zbl0132.30801
2. [2] B. APANASOV, Geometrically finite hyperbolic structures on manifolds, Ann. Global Analysis and Geometry. 1 (3) (1983), 1-22. Zbl0531.57012
3. [3] B. APANASOV, Geometrically finite groups of spatial transformations, Sibirskij Mat. J. 23 (6) (1983), 16-27 (Russian). Zbl0519.30038MR84h:30075
4. [4] B. APANASOV, Discrete transformation groups and structures of manifolds, Novosibirsk, Nauka, 1983 (Russian). Zbl0571.57002
5. [5] A. F. BEARDON and B. MASKIT, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974), 1-12. Zbl0277.30017MR48 #11489
6. [6] V. A. EFREMOVIČ and E. S. TIHOMIROVA, Equimorphisms of hyperbolic spaces, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1139-1144 (Russian). Zbl0134.16002MR29 #6374
7. [7] W. J. FLOYD, Group completions and limit sets of Kleinian groups, Inventiones Math. 57 (1980), 205-218. Zbl0428.20022MR81e:57002
8. [8] F. W. GEHRING and B. P. PALKA, Quasiconformally homogeneous domains, J. Analyse Math. 30 (1976), 50-74. Zbl0349.30019MR55 #10676
9. [9] W. HUREWICZ and H. WALLMAN, Dimension theory, Princeton University Press, Princeton, 1948. Zbl0036.12501
10. [10] W. JACO, Lectures on three-manifold topology, CBMS Conference. 43, American Mathematical Society, Providence, 1980. Zbl0433.57001MR81k:57009
11. [11] K. JOHANNSON, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics. 761, Springer-Verlag, Berlin-Heidelberg-New York, 1979. Zbl0412.57007MR82c:57005
12. [12] J. A. KELINGOS, On the maximal dilatation of quasiconformal extensions, Ann. Acad. Sci. Fenn. Ser. A I. 478 (1971), 1-8. Zbl0212.10502MR44 #430
13. [13] O. LEHTO and K. I. VIRTANEN, Quasiconformal mappings in the plane, Springer-Verlag, Berlin-Heidelberg-New York, 1973. Zbl0267.30016MR49 #9202
14. [14] A. MARDEN, The geometry of finitely generated kleinian groups, Annals of Math. 99 (1974), 383-462. Zbl0282.30014MR50 #2485
15. [15] A. MARDEN, Isomorphisms between fuchsian groups, in Advances in complex function theory, ed. by W. KIRWAN & L. ZALCMAN, Lecture Notes in Mathematics 505, Springer Verlag, Berlin-Heidelberg-New York, 1976, 56-78. Zbl0335.20024MR54 #540
16. [16] A. MARDEN and B. MASKIT, On the isomorphism theorem for Kleinian groups, Inventiones Math. 51 (1979), 9-14. Zbl0399.30037MR80f:30037
17. [17] G. A. MARGULIS, Isometry of closed manifolds of constant negative curvature with the same fundamental group, Dokl. Akad. Nauk SSSR. 192 (1979), 736-737 (= Soviet Math. Dokl. 11 (1970), 722-723). Zbl0213.48202MR42 #1012
18. [18] B. MASKIT, On boundaries of Teichmüller spaces and on kleinian groups: II, Annals of Math. 91 (1970), 607-639. Zbl0197.06003MR45 #7045
19. [19] B. MASKIT, Intersections of component subgroups of Kleinian groups, in Discontinuous groups and Riemann surfaces, ed. by L. GREENBERG, Annals of Mathematics Studies. 79, Princeton University Press, Princeton, 1974, 349-367. Zbl0305.30021MR50 #7514
20. [20] B. MASKIT, Isomorphisms of function groups, J. Analyse Math. 32 (1977), 63-82. Zbl0392.30028MR57 #3381
21. [21] B. MASKIT, On the classification of Kleinian groups II-Signatures, Acta Math. 138 (1977), 17-42. Zbl0358.30011MR56 #3288b
22. [22] G. D. MOSTOW, Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 53-104. Zbl0189.09402MR38 #4679
23. [23] G. D. MOSTOW, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies. 78, Princeton University Press, Princeton, 1973. Zbl0265.53039MR52 #5874
24. [24] J. NIELSEN, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927), 189-358. Zbl53.0545.12JFM53.0545.12
25. [25] G. PRASAD, Strong rigidity of Q-rank I lattices, Inventiones Math. 21 (1973), 255-286. Zbl0264.22009MR52 #5875
26. [26] H. M. REIMANN, Invariant extension of quasiconformal deformations, to appear. Zbl0592.30025
27. [27] A. SELBERG, On discontinuous groups in higher-dimensional symmetric spaces, in Contributions to function theory, TATA Inst. of Fund. Research, Bombay, 1960, 147-164. Zbl0201.36603MR24 #A188
28. [28] D. SULLIVAN, Hyperbolic geometry and homeomorphisms, in Geometric topology, Proceedings of the 1977 Georgia Topology Conference, ed. by J. C. CANTRELL, Academic Press, New York-London, 1979, 543-555. Zbl0478.57007MR81m:57012
29. [29] W. P. THURSTON, The geometry and topology of three-manifolds, Mimeographed lecture notes, Princeton, 1980. 
30. [30] P. TUKIA, On discrete groups of the unit disk and their isomorphisms, Ann. Acad. Sci. Fenn. Ser. AI. 504 (1972), 1-45. Zbl0225.30022MR46 #5613
31. [31] P. TUKIA, Extension of boundary homeomorphisms of discrete groups of the unit disk, Ibid. 548 (1973), 1-16. Zbl0265.30023MR49 #3123
32. [32] P. TUKIA, Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta Math. 154 (1985). Zbl0562.30018MR86f:30024
33. [33] P. TUKIA, The Hausdorff dimension of the limit set of a geometrically finite Kleinian group, Acta Math. 152 (1984), 127-140. Zbl0539.30034MR85m:30031
34. [34] P. TUKIA, Rigidity theorems for Möbius groups, to appear. Zbl0674.30038
35. [35] P. TUKIA, Differentiability and rigidity of Möbius groups, to appear. Zbl0564.30033
36. [36] P. TUKIA, On limit sets of geometrically finite Möbius groups, Math. Scandinavica, to appear. 
37. [37] P. TUKIA and J. VÄISÄLÄ, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I. 5 (1980) 97-114. Zbl0403.54005MR82g:30038
38. [38] P. TUKIA and J. VÄISÄLÄ, Lipschitz and quasiconformal approximation and extension, Ibid. 6 (1981), 303-342. Zbl0448.30021MR84a:57016
39. [39] P. TUKIA and J. VÄISÄLÄ, Quasiconformal extension from dimension n to n + 1, Annals of Math. 115 (1982), 331-348. Zbl0484.30017MR84i:30030
40. [40] J. VÄISÄLÄ, Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics. 229, Springer-Verlag, Berlin-Heidelberg-New York, 1971. Zbl0221.30031MR56 #12260
41. [41] N. J. WIELENBERG, Discrete Moebius groups : Fundamental polyhedra and convergence, American J. of Math. 99 (1977), 861-877. Zbl0373.57024MR57 #16579
42. [42] J. A. WOLF, Spaces of constant curvature, Publish or Perish Inc., Berkeley, 1977. 

1. Pekka Tukia, The limit map of a homomorphism of discrete Möbius groups
2. B. Stratmann, Mariusz Urbański, The box-counting dimension for geometrically finite Kleinian groups