The arc metric on Teichm\"uller spaces of surfaces of infinite type with boundary

Qiyu Chen; Lixin Liu

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arXiv · 1612.04213

The arc metric on Teichm\"uller spaces of surfaces of infinite type with boundary

Qiyu Chen·Lixin Liu

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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 Teichm\"uller 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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BibTeX RIS

Qiyu Chen, Lixin Liu. 2016-12-13. The arc metric on Teichm\"uller spaces of surfaces of infinite type with boundary. https://arxiv.org/abs/1612.04213

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