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January 2018 The arc metric on Teichmüller spaces of surfaces of infinite type with boundary
Qiyu Chen, Lixin Liu
Osaka J. Math. 55(1): 1-38 (January 2018).

Abstract

Let $X_{0}$ be a complete hyperbolic surface of infinite type with geodesic boundary which admits a countable pair of pants decomposition. As an application of the Basmajian identity for complete bordered hyperbolic surfaces of infinite type with limit sets of 1-dimensional measure zero, we define an asymmetric metric (which is called arc metric) on the quasiconformal Teichmüller space $\mathcal{T}(X_{0})$ provided that $X_{0}$ satisfies a geometric condition. Furthermore, we construct several examples of hyperbolic surfaces of infinite type satisfying the geometric condition and discuss the relation between the Shiga's condition and the geometric condition.

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Qiyu Chen. Lixin Liu. "The arc metric on Teichmüller spaces of surfaces of infinite type with boundary." Osaka J. Math. 55 (1) 1 - 38, January 2018.

Information

Published: January 2018
First available in Project Euclid: 11 January 2018

zbMATH: 06848741
MathSciNet: MR3744973

Subjects:
Primary: 32G15
Secondary: 30F30 , 30F60

Rights: Copyright © 2018 Osaka University and Osaka City University, Departments of Mathematics

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Vol.55 • No. 1 • January 2018
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