The limit map of a homomorphism of discrete Möbius groups
Tukia, Pekka
Publications Mathématiques de l'IHÉS, Tome 82 (1995), p. 97-132 / Harvested from Numdam
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Publié le : 1995-01-01
@article{PMIHES_1995__82__97_0,
     author = {Tukia, Pekka},
     title = {The limit map of a homomorphism of discrete M\"obius groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {82},
     year = {1995},
     pages = {97-132},
     mrnumber = {98e:57052},
     zbl = {0858.30034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1995__82__97_0}
}

Tukia, Pekka. The limit map of a homomorphism of discrete Möbius groups. Publications Mathématiques de l'IHÉS, Tome 82 (1995) pp. 97-132. http://gdmltest.u-ga.fr/item/PMIHES_1995__82__97_0/

[BM] A. F. Beardon and B. Maskit, Limit points of Kleinian groups and finite sided fundamental polyhedra, Acta Math., 132 (1974), 1-12. | MR 48 #11489 | Zbl 0277.30017

[B] F. Bonahon, Bouts des variétés hyperboliques de dimension 3, Ann. Math., 124 (1986), 71-158. | MR 88c:57013 | Zbl 0671.57008

[CT] J. W. Cannon and W. P. Thurston, Group invariant Peano curves, Manuscript.

[FE] H. Federer, Geometric measure theory, Springer-Verlag, 1969. | MR 41 #1976 | Zbl 0176.00801

[FL] W. J. Floyd, Group completions and limit sets of Kleinian groups, Inventions math., 57 (1980), 205-218. | MR 81e:57002 | Zbl 0428.20022

[GM] F. W. Gehring and G. J. Martin, Discrete quasiconformal groups. I, Proc. London. Math. Soc. (3) 55 (1987), 331-358. | MR 88m:30057 | Zbl 0628.30027

[M] G. J. Martin, Infinite group actions on spheres, Rev. Math. Iberoamericana, 4 (1988), 407-451. | MR 91b:57043 | Zbl 0693.57020

[MT] G. J. Martin and P. Tukia, Convergence and Möbius groups, in Holomorphic Functions and Moduli II, ed. by D. Drasin et al., MSRI Publications 11 (1988), 87-140. | MR 89m:30095 | Zbl 0659.30036

[MA] B. Maskit, On boundaries of Teichmüller spaces and on kleinian groups : II, Ann. Math., 91 (1970), 607-639. | MR 45 #7045 | Zbl 0197.06003

[M1] P. J. Myrberg, Ein Approximationssatz für die Fuchsschen Gruppen, Acta Math., 57 (1931), 389-401. | JFM 57.0450.02 | Zbl 0003.06303

[M2] P. J. Myrberg, Die Kapazität der singulären Menge der linearen Gruppen, Ann. Acad. Sci. Fenn., Ser. A I, 10 (1941), 1-19. | JFM 67.0287.01 | Zbl 0027.21703

[NE] R. Nevanlinna, Analytic Functions, Springer-Verlag, 1970. | MR 43 #5003 | Zbl 0199.12501

[NI] P. J. Nicholls, The ergodic theory of discrete groups, London Mathematical Society Lecture Notes Series, 143 (1989). | MR 91i:58104 | Zbl 0674.58001

[P] S. J. Patterson, The limit set of a Fuchsian group, Acta Math., 136 (1976), 241-273. | MR 56 #8841 | Zbl 0336.30005

[S1] D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Publ. Math. Inst. Hautes Étud. Sci., 50 (1979), 171-202. | Numdam | MR 81b:58031 | Zbl 0439.30034

[S2] D. Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math., 153 (1984), 259-277. | MR 86c:58093 | Zbl 0566.58022

[T] W. P. Thurston, The geometry and topology of three-manifolds, Lecture Notes at the University of Princeton, 1980.

[T1] P. Tukia, The Hausdorff dimension of the limit set of a geometrically finite Kleinian group, Acta Math., 152 (1984), 127-140. | MR 85m:30031 | Zbl 0539.30034

[T2] P. Tukia, On isomorphisms of geometrically finite Kleinian groups, Publ. Math. Inst. Hautes Étud. Sci., 61 (1985), 171-214. | Numdam | MR 87j:30110 | Zbl 0572.30036

[T3] P. Tukia, A remark on a paper by Floyd, in Holomorphic functions and moduli, II, ed. by D. Drasin et al., MSRI Publications, 11 (1988), 165-172. | MR 90b:30054 | Zbl 0653.30027

[T4] P. Tukia, A rigidity theorem for Möbius groups, Inventiones math., 97 (1989), 405-431. | MR 90i:20051 | Zbl 0674.30038

[T5] P. Tukia, The Poincaré series and the conformal measure of conical and Myrberg limit points, J. Anal. Math., 62 (1994), 241-259. | MR 97c:30047 | Zbl 0799.30035

[T6] P. Tukia, On discrete groups of the unit disk and their isomorphisms, Ann. Acad. Sci. Fenn., Ser. A I, 504 (1972), 1-45. | MR 46 #5613 | Zbl 0225.30022

[T7] P. Tukia, On the dimension of limit sets of geometrically finite Möbius groups, Ann. Acad. Sci. Fenn., Ser. A I, 19 (1994), 11-24. | MR 95i:30035 | Zbl 0789.30032

[T8] P. Tukia, Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta Math., 154 (1985), 153-193. | MR 86f:30024 | Zbl 0562.30018

[T9] P. Tukia, Convergence groups and Gromov's hyperbolic metric spaces, New Zealand J. Math., 23 (1994), 157-187. | MR 96c:30042 | Zbl 0855.30036