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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1007/978-3-658-00998-4_91

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1869-1862

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Convex hull of set in thick part of Teichmüller sp

Authors: LiXin Liu Hiroshige Shiga ZongLiang Sun
Publish Date: 2014/07/04
Volume: 57, Issue: 9, Pages: 1799-1810
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Abstract

Let X be a nonelementary Riemann surface of type g n where g is the number of genus and n is the number of punctures with 3g3+n 1 Let TX be the Teichmüller space of X By constructing a certain subset E of TX we show that the convex hull of E with respect to the Teichmüller metric the Carathéodory metric and the WeilPetersson metric is not in any thick part of the Teichmüller space respectively This implies that convex hulls of thick part of Teichmüller space with respect to these metrics are not always in thick part of Teichmüller space as well as the facts that thick part of Teichmüller space is not always convex with respect to these metrics

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