Nonextendability of the Bers isomorphism
HTML articles powered by AMS MathViewer
- by Chaohui Zhang
- Proc. Amer. Math. Soc. 123 (1995), 2451-2458
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249895-0
- PDF | Request permission
Abstract:
Let G be a torsion free finitely generated Fuchsian group of the first kind of type (p, n). The purpose of this paper is to show that the Bers isomorphism of the Bers fiber space $F(G)$ onto the Bers embedding of $T(\dot G)$ has no continuous extension to the boundary, provided that $\dim T(G) \geq 1$, where Ġ is another torsion free finitely generated Fuchsian group of the first kind of type $(p,n + 1)$.References
- William Abikoff, Degenerating families of Riemann surfaces, Ann. of Math. (2) 105 (1977), no. 1, 29–44. MR 442293, DOI 10.2307/1971024
- Lipman Bers, Fiber spaces over Teichmüller spaces, Acta Math. 130 (1973), 89–126. MR 430318, DOI 10.1007/BF02392263
- Lipman Bers, On iterates of hyperbolic transformations of Teichmüller space, Amer. J. Math. 105 (1983), no. 1, 1–11. MR 692104, DOI 10.2307/2374379
- Lipman Bers, An extremal problem for quasiconformal mappings and a theorem by Thurston, Acta Math. 141 (1978), no. 1-2, 73–98. MR 477161, DOI 10.1007/BF02545743
- Clifford J. Earle and Irwin Kra, On holomorphic mappings between Teichmüller spaces, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 107–124. MR 0430319
- Irwin Kra, On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces, Acta Math. 146 (1981), no. 3-4, 231–270. MR 611385, DOI 10.1007/BF02392465
- Bernard Maskit, On boundaries of Teichmüller spaces and on Kleinian groups. II, Ann. of Math. (2) 91 (1970), 607–639. MR 297993, DOI 10.2307/1970640
- Subhashis Nag, Nongeodesic discs embedded in Teichmüller spaces, Amer. J. Math. 104 (1982), no. 2, 399–408. MR 654412, DOI 10.2307/2374164
- H. L. Royden, Automorphisms and isometries of Teichmüller space, Advances in the Theory of Riemann Surfaces (Proc. Conf., Stony Brook, N.Y., 1969) Ann. of Math. Studies, No. 66, Princeton Univ. Press, Princeton, N.J., 1971, pp. 369–383. MR 0288254
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2451-2458
- MSC: Primary 32G15; Secondary 30F60
- DOI: https://doi.org/10.1090/S0002-9939-1995-1249895-0
- MathSciNet review: 1249895