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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)



Extremal length boundary of the Teichmüller space contains non-Busemann points

Author: Hideki Miyachi
Journal: Trans. Amer. Math. Soc. 366 (2014), 5409-5430
MSC (2010): Primary 30F60, 32G15, 30C75, 31B15; Secondary 30C62, 51F99
Published electronically: May 21, 2014
MathSciNet review: 3240928
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Abstract: We present an overview of the extremal length embedding of a Teichmüller space and its extremal length compactification. For Teichmüller spaces of dimension at least two, we describe a large class of non-Busemann points on the metric boundary, that is, points that cannot be realized as limits of almost geodesic rays.

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Additional Information

Hideki Miyachi
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043, Japan

Keywords: Teichm\"uller space, Teichm\"uller distance, extremal length, metric boundary, horofunction boundary, Busemann point
Received by editor(s): March 31, 2012
Received by editor(s) in revised form: August 23, 2012, and December 8, 2012
Published electronically: May 21, 2014
Additional Notes: The author was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 21540177
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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