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Incompleteness of the pressure metric on the Teichmüller space of a bordered surface

Published online by Cambridge University Press:  28 September 2017

BINBIN XU
BINBIN XU*
Affiliation:
Korea Institute for Advanced Study (KIAS), 85 Hoegi-ro, Dongdaemun-gu, 02455 Seoul, Republic of Korea email xubin@kias.re.kr
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Abstract

We prove that the pressure metric on the Teichmüller space of a bordered surface is incomplete and that a completion can be given by the moduli space of metrics on a graph (dual to a special ideal triangulation of the same bordered surface) equipped with pressure metric. In contrast to the closed surface case, we obtain as a corollary that the pressure metric is not bi-Lipschitz to the Weil–Petersson metric.

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Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 6 , June 2019 , pp. 1710 - 1728
Copyright
© Cambridge University Press, 2017 

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