## Kodai Mathematical Journal

### The effect of Fenchel-Nielsen coordinates under elementary moves

#### Abstract

We describe the effect of Fenchel-Nielsen coordinates under elementary move for hyperbolic surfaces with geodesic boundaries, punctures and cone points, which generalize Okai's result for surfaces with geodesic boundaries. The proof relies on the parametrization of the Teichmüller space of surface of type (1,1) or (0,4) as a sub-locus of an algebraic equation in $\mathbf{R}^3$. As an application, we show that the hyperbolic length functions of closed curves are asymptotically piecewise linear functions with respect to the Fenchel Nielsen coordinates in the Teichmüller spaces of surfaces with cone points.

#### Article information

Source
Kodai Math. J., Volume 41, Number 2 (2018), 421-439.

Dates
First available in Project Euclid: 2 July 2018

https://projecteuclid.org/euclid.kmj/1530496851

Digital Object Identifier
doi:10.2996/kmj/1530496851

Mathematical Reviews number (MathSciNet)
MR3824860

Zentralblatt MATH identifier
06936462

#### Citation

Tan, Dong; Liu, Peijia; Liu, Xuewen. The effect of Fenchel-Nielsen coordinates under elementary moves. Kodai Math. J. 41 (2018), no. 2, 421--439. doi:10.2996/kmj/1530496851. https://projecteuclid.org/euclid.kmj/1530496851