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On the horocyclic coordinate for the Teichmüller space of once punctured tori


Author: Hideki Miyachi
Journal: Proc. Amer. Math. Soc. 130 (2002), 1019-1029
MSC (2000): Primary 30F40, 32G15
DOI: https://doi.org/10.1090/S0002-9939-01-06170-6
Published electronically: November 28, 2001
MathSciNet review: 1873775
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Abstract: This paper deals with analytic and geometric properties of the Maskit embedding of the Teichmüller space of once punctured tori. We show that the image of this embedding has an inward-pointing cusp and study the boundary behavior of conformal automorphisms. These results are proved using Y.N. Minsky's Pivot Theorem.


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  • 1. Y. Imayoshi and M. Taniguchi, An introduction to Teichmüller spaces, Springer-Verlag (1991). MR 94b:32031
  • 2. L. Keen and C.Series, Pleating coordinates for the Maskit embedding of the Teichmüller space of puncture tori, Topology Vol 32, no 4 (1993), 719-749. MR 95g:32030
  • 3. L. Keen, B.Maskit, and C.Series, Geometric finiteness and uniqueness for Kleinian groups with circle packing limit sets, J. reine. angew. Math. 436(1993), 209-219. MR 94b:30053
  • 4. S. Kerckhoff and P. W. Thurston, Non-continuity of the action of the modular groups at Ber's boundary of Teichmüller space, Invent. Math., Vol.100, 25-47. MR 91a:57038
  • 5. I. Kra, Non-variational global coordinates for Teichmüller spaces, Holomorphic functions and Moduli II, pages 221-249, Springer-Verlag: MSRI publications volume 10 (1988). MR 90b:32044
  • 6. -, Horocyclic coordinates for Riemann surfaces and Moduli spaces I: Teichmüller and Riemann spaces of Kleinian groups, Jour. of Amer. Math. Soc. Vol 3 (1990), 499-578. MR 91c:32014
  • 7. B.Maskit, Moduli of Marked Riemann surfaces, Bull.A.M.S.,80 (1974), 773-777. MR 49:10875
  • 8. B.Maskit, Comparison of hyperbolic and extremal lengths, Ann.Acad.Sci.Fenn. Series A., Vol.10 (1985), 381-386. MR 87c:30062
  • 9. -, Kleinian groups, Springer-Verlag (1987). MR 90a:30132
  • 10. K. Matsuzaki and M. Taniguchi, Hyperbolic manifolds and Kleinian groups, Oxford Mathematical Monograph, (1998). MR 99g:30055
  • 11. C.T.McMullen, Renormalization and 3-Manifolds which Fiber over the circle, Princeton University Press, Study 142, (1996). MR 97f:57022
  • 12. Y.N.Minsky, The classification of punctured torus groups, Ann.of Math.149, 559-626 (1999). MR 2000f:30028
  • 13. H.Miyachi, Cusps in complex boundaries of one-dimensional Teichmüller space, submitted, (2000).
  • 14. S.Nag Complex analytic theory of Teichmüller spaces, Wiley, NewYork, (1988). MR 89f:32040
  • 15. C.Series Lectures on Pleating coordinates for once punctured tori, lecture notes on the conference (organized by Y.Komori) in Osaka City University in July 1998.
  • 16. Ch. Pommerenke, Boundary behavior of conformal maps, Springer-Verlag (1991). MR 95b:30008
  • 17. M. Tsuji, Potential Theory in Modern Function Theory, Maruzen (1959). MR 22:5712
  • 18. M.Wada, OPTi3.0, http://vivaldi.ics.nara-wu.ac.jp/ wada/OPTi/.
  • 19. D.J.Wright, The shape of the boundary of Maskit's embedding of the Teichmüller space of once punctured tori, preprint (1988).

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Additional Information

Hideki Miyachi
Affiliation: Department of Mathematics, Osaka City University, Sumiyoshi, Osaka 558-8585, Japan
Email: miyaji@sci.osaka-cu.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-01-06170-6
Received by editor(s): May 25, 1999
Received by editor(s) in revised form: September 25, 2000
Published electronically: November 28, 2001
Additional Notes: The author is partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists from April, 2000.
Dedicated: Dedicated to Professor Hiroki Sato on the occasion of his sixtieth birthday
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2001 Hideki Miyachi

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