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Vertical limits of graph domains


Authors: Hrant Hakobyan and Dragomir Šarić
Journal: Proc. Amer. Math. Soc. 144 (2016), 1223-1234
MSC (2010): Primary 30F60; Secondary 30C62, 32G15
DOI: https://doi.org/10.1090/proc12780
Published electronically: August 18, 2015
MathSciNet review: 3447674
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Abstract: We consider the limiting behavior of Teichmüller geodesics in the universal Teichmüller space $ T(\mathbb{H})$. Our main result states that the limits of the Teichmüller geodesics in the Thurston's boundary of $ T(\mathbb{H})$ may depend on both vertical and horizontal foliation of the corresponding holomorphic quadratic differential.


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Additional Information

Hrant Hakobyan
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: hakobyan@math.ksu.edu

Dragomir Šarić
Affiliation: Department of Mathematics, Queens College of CUNY, 65-30 Kissena Boulevard, Flushing, New York 11367 – and – Mathematics PhD Program, The CUNY Graduate Center, 365 Fifth Avenue, New York, New York 10016-4309
Email: Dragomir.Saric@qc.cuny.edu

DOI: https://doi.org/10.1090/proc12780
Received by editor(s): September 9, 2014
Received by editor(s) in revised form: September 10, 2014, and March 10, 2015
Published electronically: August 18, 2015
Additional Notes: The first author was partially supported by Kansas NSF EPSCoR Grant NSF68311
The second author was partially supported by National Science Foundation grant DMS 1102440 and by the Simons Foundation Collaboration Grant for Mathematicians 2011
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society

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