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June 2018 The effect of Fenchel-Nielsen coordinates under elementary moves
Dong Tan, Peijia Liu, Xuewen Liu
Kodai Math. J. 41(2): 421-439 (June 2018). DOI: 10.2996/kmj/1530496851

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.

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Dong Tan. Peijia Liu. Xuewen Liu. "The effect of Fenchel-Nielsen coordinates under elementary moves." Kodai Math. J. 41 (2) 421 - 439, June 2018. https://doi.org/10.2996/kmj/1530496851

Information

Published: June 2018
First available in Project Euclid: 2 July 2018

zbMATH: 06936462
MathSciNet: MR3824860
Digital Object Identifier: 10.2996/kmj/1530496851

Rights: Copyright © 2018 Tokyo Institute of Technology, Department of Mathematics

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Vol.41 • No. 2 • June 2018
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