The horofunction compactification of the arc metric on Teichm\"uller space

Daniele Alessandrini; Lixin Liu; Athanase Papadopoulos; Weixu Su

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arXiv · 1411.6208

The horofunction compactification of the arc metric on Teichm\"uller space

Daniele Alessandrini·Lixin Liu·Athanase Papadopoulos·Weixu Su

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Abstract

The arc metric is an asymmetric metric on the Teichm{\"u}ller space T(S) of a surface S with nonempty boundary. In this paper we study the relation between Thurston's compactification and the horofunction compactification of T(S) endowed with the arc metric. We prove that there is a natural homeomorphism between the two compactifications.

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Daniele Alessandrini, Lixin Liu, Athanase Papadopoulos, Weixu Su. 2014-11-23. The horofunction compactification of the arc metric on Teichm\"uller space. https://arxiv.org/abs/1411.6208

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