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On the Teichmüller theorem and the heights theorem for quadratic differentials


Author: Shengjian Wu
Journal: Proc. Amer. Math. Soc. 129 (2001), 765-770
MSC (2000): Primary 30F10, 30F60
DOI: https://doi.org/10.1090/S0002-9939-00-05579-9
Published electronically: August 30, 2000
MathSciNet review: 1707534
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Abstract | References | Similar Articles | Additional Information

Abstract: By using the Marden-Strebel heights theorem for quadratic differentials, we provide a concrete method for finding the Teichmüller differential associated with the Teichmüller mapping between compact or finitely punctured Riemann surfaces.


References [Enhancements On Off] (What's this?)

  • [1] F. Gardiner, Teichmüller theory and quadratic differentials, Wiley, New York, 1987. MR 88m:32044
  • [2] A. Marden and K. Strebel, The heights theorem for quadratic differentials on Riemann surfaces, Acta Math., 153(1984), 153-211. MR 86a:30076
  • [3] A. Marden and K. Strebel, A characterization of Teichmüller differentials, J. Differential Geometry, 37(1993), 1-29. MR 93m:32028
  • [4] K. Strebel, The elementary cases in Teichmüller mapping theorem, Ann. Acad. Sci. Fenn., Series A.I. Math., 15(1990), 319-328. MR 91m:30056

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Additional Information

Shengjian Wu
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: wusj@pku.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-00-05579-9
Keywords: Quasiconformal mapping, Teichm\"{u}ller differential, Hamilton sequence, quadratic differentials
Received by editor(s): March 6, 1999
Received by editor(s) in revised form: May 6, 1999
Published electronically: August 30, 2000
Additional Notes: This work was supported by the SRF for ROCS, SEM and the NSF of China
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society

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