Abstract
Let X = ℂ\{0, 1} and \(\dot X = X\backslash \left\{ {\hat a} \right\}\). We get a necessary and sufficient condition on the position of \(\hat a\) in X such that \(\dot X\) has stable Teichmüller mappings. Furthermore, we can formulate all these stable Teichmüller mappings. The main result in this paper partially answers a question posed by Kra.
Similar content being viewed by others
References
Bers L. An extremal problem for quasiconformal mappings and a theorem by Thurston. Acta Math, 1978, 141: 73–98
Imayoshi Y, Taniguchi M. An Introduction to Teichmüller Spaces. Berlin: Springer-Verlag, 1992
Kra I. On the Nielsen-Thurston-Bers type of some self-maps of Riemann surfaces. Acta Math, 1981, 146: 231–270
Kravetz S. On the geometry of Teichmüller spaces and the structure of their modular groups. Ann Aead Sci Fenn, 1959, 278: 1–35
Marden A, Strebel K. Pseudo-Anosov Teichmüller mappings. J Anal Math, 1986, 46: 194–220
Nag S. The Complex Analytic Theory of Teichmüller Spaces. New York: Wiley, 1988
Strebel K. Quadratic Differentials. Berlin: Springer-Verlag, 1984
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, Y., Wu, S. Stable Teichmüller mappings of type (0, 4). Sci. China Math. 54, 1379–1388 (2011). https://doi.org/10.1007/s11425-011-4202-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-011-4202-0