Some special limits of Schottky groups

Gallo, Daniel M.

doi:10.1090/S0002-9939-1993-1148024-X

Some special limits of Schottky groups
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Proc. Amer. Math. Soc. 118 (1993), 877-883 Request permission

Abstract:

We show that every extended Schottky group $G$ which uniformizes a compact Riemann surface $S$ is a geometric limit of Schottky groups ${G_n}$ which also uniformize $S$. That is, every element $g \in G$ is the limit of elements ${g_n} \in {G_n}$.

References

R. C. Gunning, Affine and projective structures on Riemann surfaces, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 225–244. MR 624816
Dennis A. Hejhal, On Schottky and Teichmüller spaces, Advances in Math. 15 (1975), 133–156. MR 357862, DOI 10.1016/0001-8708(75)90128-0
Troels Jørgensen, On discrete groups of Möbius transformations, Amer. J. Math. 98 (1976), no. 3, 739–749. MR 427627, DOI 10.2307/2373814
Troels Jørgensen and Peter Klein, Algebraic convergence of finitely generated Kleinian groups, Quart. J. Math. Oxford Ser. (2) 33 (1982), no. 131, 325–332. MR 668178, DOI 10.1093/qmath/33.3.325
Irwin Kra, Deformations of Fuchsian groups. II, Duke Math. J. 38 (1971), 499–508. MR 285734
Irwin Kra, Families of univalent functions and Kleinian groups, Israel J. Math. 60 (1987), no. 1, 89–127. MR 931871, DOI 10.1007/BF02766172
Irwin Kra and Bernard Maskit, Remarks on projective structures, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 343–359. MR 624824
Bernard Maskit, Decomposition of certain Kleinian groups, Acta Math. 130 (1973), 243–263. MR 404614, DOI 10.1007/BF02392267

Geometry and topology of

manifolds