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arXiv · 1608.03937

Incompleteness of pressure metric on Teichm\"uller space of a bordered surface

Binbin Xu
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Abstract

We prove that the pressure metric on the Teichm\"uller space of a bordered surface is incomplete and its partial completion can be given by the moduli space of metric graphs for a fat graph associated to the same bordered surface equipped with pressure metric. As a corollary, we show that the pressure metric is not a constant multiple of the Weil-Petersson metric which is different from the closed surface case.

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Binbin Xu. 2016-08-13. Incompleteness of pressure metric on Teichm\"uller space of a bordered surface. https://arxiv.org/abs/1608.03937

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