## On the straightness of reduced Teichmüller space

HTML articles powered by AMS MathViewer

- by Judith C. Wason PDF
- Proc. Amer. Math. Soc.
**56**(1976), 193-198 Request permission

## Abstract:

Under a natural injection which is shown to be an isometry, the image of the reduced Teichmüller space ${T^\# }(G)$ in the open straight Teichmüller space of the Fuchsian model of $G,T(H)$, is an open straight subspace.## References

- Lars V. Ahlfors,
*On quasiconformal mappings*, J. Analyse Math.**3**(1954), 1–58; correction, 207–208. MR**64875**, DOI 10.1007/BF02803585 - Lars V. Ahlfors,
*Lectures on quasiconformal mappings*, Van Nostrand Mathematical Studies, No. 10, D. Van Nostrand Co., Inc., Toronto, Ont.-New York-London, 1966. Manuscript prepared with the assistance of Clifford J. Earle, Jr. MR**0200442**
—, - Lipman Bers,
*Universal Teichmüller space*, Analytic methods in mathematical physics (Sympos., Indiana Univ., Bloomington, Ind., 1968) Gordon and Breach, New York, 1970, pp. 65–83. MR**0349988** - Lipman Bers,
*Extremal quasiconformal mappings*, 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. 27–52. MR**0285706** - Herbert Busemann,
*Metric Methods in Finsler Spaces and in the Foundations of Geometry*, Annals of Mathematics Studies, No. 8, Princeton University Press, Princeton, N. J., 1942. MR**0007251** - Clifford J. Earle,
*Teichmüller spaces of groups of the second kind*, Acta Math.**112**(1964), 91–97. MR**165096**, DOI 10.1007/BF02391766 - Clifford J. Earle,
*Reduced Teichmüller spaces*, Trans. Amer. Math. Soc.**126**(1967), 54–63. MR**204642**, DOI 10.1090/S0002-9947-1967-0204642-3 - Saul Kravetz,
*On the geometry of Teichmüller spaces and the structure of their modular groups*, Ann. Acad. Sci. Fenn. Ser. A I No.**278**(1959), 35. MR**0148906**
M. Linch,

*Quasiconformal mappings and Teichmüller’s theorem*, Analytic Functions, Princeton Univ. Press, Princeton, N. J., 1960, pp. 89-119.

*On metrics in Teichmüller space*, Doctoral Dissertation, Columbia University, New York, 1971. J. C. Wason,

*On geometry of Teichmüller spaces*, Doctoral Dissertation, Columbia University, New York, 1973.

## Additional Information

- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**56**(1976), 193-198 - MSC: Primary 32G15; Secondary 30A52
- DOI: https://doi.org/10.1090/S0002-9939-1976-0417457-9
- MathSciNet review: 0417457