Parametrization of Teichmüller spaces by geodesic length functions

  • Mika Seppälä
  • Tuomas Sorvali
Conference paper

DOI: 10.1007/978-1-4613-9611-6_18

Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 11)
Cite this paper as:
Seppälä M., Sorvali T. (1988) Parametrization of Teichmüller spaces by geodesic length functions. In: Drasin D., Earle C.J., Gehring F.W., Kra I., Marden A. (eds) Holomorphic Functions and Moduli II. Mathematical Sciences Research Institute Publications, vol 11. Springer, New York, NY

Abstract

The Teichmüller space T(Σ) of a compact C-surface Σ can be parametrized by geodesic length functions. More precisely, we can find a set {α1... ,αn} of closed curves αj on Σ such that the isotopy class of a hyperbolic metric d on Σ (i.e. the point [d] ∊ T(Σ)) is determined by the lengths of geodesic curves homotopic to the curves αj on (Σ, d). However, since the fundamental group of Σ is not freely generated there is a quite complicated relation among these geodesic length function.

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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Mika Seppälä
    • 1
    • 2
  • Tuomas Sorvali
    • 3
  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgDeutschland
  2. 2.Department of MathematicsUniversity of HelsinkiHelsinkiFinland
  3. 3.Department of MathematicsUniversity of JoensuuJoensuuFinland

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