Parametrizations of Teichmüller space and its Thurston boundary. (English) Zbl 1044.32005

Hildebrandt, Stefan (ed.) et al., Geometric analysis and nonlinear partial differential equations. Berlin: Springer (ISBN 3-540-44051-8/hbk). 81-88 (2003).
Let \(T_g\) \((g\geq 2)\) denote the Teichmüller space of hyperbolic metrics on a closed surface of genus \(g\), and let us denote its boundary by \(\partial T_g\). The question dealt with here is to find the minimum number of curves needed to obtain an imbedding of \(\partial T_g\) into the real projective space.
The number \(9g\)-\(9\) is well known to do this. P. Schmutz [Comment. Math. Helv. 68, 278–288 (1993; Zbl 0790.30036)] showed that for every \(g\geq 2\), the Teichmüller space \(T_g\) can be parametrized by \(6g\)-\(5\) length functions of simple closed geodesics. Here the author gives another proof of this result by simplifying the proof of Schmutz.
For the entire collection see [Zbl 1007.00073].


32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
30F60 Teichmüller theory for Riemann surfaces


Zbl 0790.30036