Geometrically finite groups of transformations of space. (English. Russian original) Zbl 0519.30038

Sib. Math. J. 23, 771-780 (1983); translation from Sib. Mat. Zh. 23, No. 6, 16-27 (1982).


30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)


Zbl 0277.30017
Full Text: DOI


[1] L. Greenberg, ?Fundamental polyhedra for Kleinian groups,? Ann. Math.,84, 433-442 (1966). · Zbl 0161.27405
[2] T. Jørgensen, ?Compact 3-manifolds of constant negative curvature fibering over the circle,? Ann. Math.,106, 61-72 (1977). · Zbl 0368.53025
[3] T. Jørgensen and A. Marden, ?Two doubly generated groups,? Q. J. Math.,30, 143-156 (1979). · Zbl 0414.30035
[4] A. Beardon and B. Maskit, ?Limit points of Kleinian groups and finite sided fundamental polyhedra,? Acta Math.,132, 1-12 (1974). · Zbl 0277.30017
[5] Chen Su-Shing, ?A theorem of Ahlfors for hyperbolic spaces,? Trans. Am. Math. Soc.,242, 401-406 (1978). · Zbl 0386.22009
[6] G. A. Hedlund, ?Fuchsian groups and transitive horocycles,? Duke Math. J.,2, 530-542 (1936). · JFM 62.0392.03
[7] B. N. Apanasov, ?On an analytic method in the theory of Kleinian groups of a multidimensional Euclidean space,? Dokl. Akad. Nauk SSSR,222, 11-14 (1975).
[8] B. N. Apanasov, ?Entire automorphic forms in Rn,? Sib. Mat. Zh.,19, 735-748 (1978).
[9] B. N. Apanasov, ?On Kleinian groups in space,? Sib. Mat. Zh.,16, 891-898 (1975).
[10] J. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York (1967). · Zbl 0162.53304
[11] B. Maskit, ?On boundaries of Teichmüller spaces and on Kleinian groups. II,? Ann. Math.,91, 607-639 (1970). · Zbl 0197.06003
[12] B. N. Apanasov, ?Nontriviality of Teichmüller space for Kleinian groups in space,? in: Proceedings of the 1978 Stony Brook conference: Riemann Surfaces and Related Topics, Princeton Univ. Press, Princeton (1981), pp. 21-31.
[13] N. J. Wilenberg, ?Discrete Moebius groups: fundamental polyhedra and convergence,? Am. J. Math.,99, 861-877 (1977). · Zbl 0373.57024
[14] A. Marden, ?The geometry of finitely generated Kleinian groups,? Ann. Math.,99, 383-462 (1974). · Zbl 0282.30014
[15] B. N. Apanasov, ?On a class of Kleinian groups inR n,?, Dokl. Akad. Nauk SSSR,215, 509-510 (1974).
[16] L. V. Ahlfors, ?Fundamental polyhedrons and limit point sets of Kleinian groups,? Proc. Natl. Acad. Sci. USA,55, 251-254 (1966). · Zbl 0132.30801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.