On isomorphisms of geometrically finite Möbius groups

Tukia, Pekka

Publications Mathématiques de l'IHÉS, Tome 61 (1985), pp. 171-214.

[1] L. V. Ahlfors, Fundamental polyhedrons and limit point sets of Kleinian groups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 251-254. | Zbl

[2] B. Apanasov, Geometrically finite hyperbolic structures on manifolds, Ann. Global Analysis and Geometry. 1 (3) (1983), 1-22. | Zbl

[3] B. Apanasov, Geometrically finite groups of spatial transformations, Sibirskij Mat. J. 23 (6) (1983), 16-27 (Russian). | MR | Zbl

[4] B. Apanasov, Discrete transformation groups and structures of manifolds, Novosibirsk, Nauka, 1983 (Russian). | Zbl

[5] A. F. Beardon and B. Maskit, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math. 132 (1974), 1-12. | MR | Zbl

[6] V. A. Efremovič and E. S. Tihomirova, Equimorphisms of hyperbolic spaces, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1139-1144 (Russian). | MR | Zbl

[7] W. J. Floyd, Group completions and limit sets of Kleinian groups, Inventiones Math. 57 (1980), 205-218. | MR | Zbl

[8] F. W. Gehring and B. P. Palka, Quasiconformally homogeneous domains, J. Analyse Math. 30 (1976), 50-74. | MR | Zbl

[9] W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press, Princeton, 1948. | Zbl

[10] W. Jaco, Lectures on three-manifold topology, CBMS Conference. 43, American Mathematical Society, Providence, 1980. | MR | Zbl

[11] K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics. 761, Springer-Verlag, Berlin-Heidelberg-New York, 1979. | MR | Zbl

[12] J. A. Kelingos, On the maximal dilatation of quasiconformal extensions, Ann. Acad. Sci. Fenn. Ser. A I. 478 (1971), 1-8. | MR | Zbl

[13] O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, Springer-Verlag, Berlin-Heidelberg-New York, 1973. | MR | Zbl

[14] A. Marden, The geometry of finitely generated kleinian groups, Annals of Math. 99 (1974), 383-462. | MR | Zbl

[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. | MR | Zbl

[16] A. Marden and B. Maskit, On the isomorphism theorem for Kleinian groups, Inventiones Math. 51 (1979), 9-14. | MR | Zbl

[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). | MR | Zbl

[18] B. Maskit, On boundaries of Teichmüller spaces and on kleinian groups: II, Annals of Math. 91 (1970), 607-639. | MR | Zbl

[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. | MR | Zbl

[20] B. Maskit, Isomorphisms of function groups, J. Analyse Math. 32 (1977), 63-82. | MR | Zbl

[21] B. Maskit, On the classification of Kleinian groups II-Signatures, Acta Math. 138 (1977), 17-42. | MR | Zbl

[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. | Numdam | MR | Zbl

[23] G. D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies. 78, Princeton University Press, Princeton, 1973. | MR | Zbl

[24] J. Nielsen, Untersuchungen zur Topologie der geschlossenen zweiseitigen Flächen, Acta Math. 50 (1927), 189-358. | JFM

[25] G. Prasad, Strong rigidity of Q-rank I lattices, Inventiones Math. 21 (1973), 255-286. | MR | Zbl

[26] H. M. Reimann, Invariant extension of quasiconformal deformations, to appear. | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[29] W. P. Thurston, The geometry and topology of three-manifolds, Mimeographed lecture notes, Princeton, 1980.

[30] P. Tukia, On discrete groups of the unit disk and their isomorphisms, Ann. Acad. Sci. Fenn. Ser. AI. 504 (1972), 1-45. | MR | Zbl

[31] P. Tukia, Extension of boundary homeomorphisms of discrete groups of the unit disk, Ibid. 548 (1973), 1-16. | MR | Zbl

[32] P. Tukia, Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta Math. 154 (1985). | MR | Zbl

[33] P. Tukia, The Hausdorff dimension of the limit set of a geometrically finite Kleinian group, Acta Math. 152 (1984), 127-140. | MR | Zbl

[34] P. Tukia, Rigidity theorems for Möbius groups, to appear. | Zbl

[35] P. Tukia, Differentiability and rigidity of Möbius groups, to appear. | Zbl

[36] P. Tukia, On limit sets of geometrically finite Möbius groups, Math. Scandinavica, to appear.

[37] P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I. 5 (1980) 97-114. | MR | Zbl

[38] P. Tukia and J. Väisälä, Lipschitz and quasiconformal approximation and extension, Ibid. 6 (1981), 303-342. | MR | Zbl

[39] P. Tukia and J. Väisälä, Quasiconformal extension from dimension n to n + 1, Annals of Math. 115 (1982), 331-348. | MR | Zbl

[40] J. Väisälä, Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics. 229, Springer-Verlag, Berlin-Heidelberg-New York, 1971. | MR | Zbl

[41] N. J. Wielenberg, Discrete Moebius groups : Fundamental polyhedra and convergence, American J. of Math. 99 (1977), 861-877. | MR | Zbl

[42] J. A. Wolf, Spaces of constant curvature, Publish or Perish Inc., Berkeley, 1977.