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Volume 30, Issue 1
A Sufficient Condition for Rigidity in Extremality of Teichmüller Equivalence Classes by Schwarzian Derivative

M. Yanagishita

DOI: 10.4208/ata.2014.v30.n1.9

Anal. Theory Appl., 30 (2014), pp. 130-135.

Published online: 2014-03

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  • Abstract

The Strebel point is a Teichmüller equivalence class in the Teichmüller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmüller equivalence class of the universal Teichmüller space under which the class is a Strebel point. As an application, we construct a Teichmüller equivalence class that is a Strebel point and that is not an asymptotically conformal class.

  • Keywords

Strebel points, the Schwarzian derivative, asymptotically conformal maps.

  • AMS Subject Headings

30F60, 30C62

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-30-130, author = {M. Yanagishita}, title = {A Sufficient Condition for Rigidity in Extremality of Teichmüller Equivalence Classes by Schwarzian Derivative}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {1}, pages = {130--135}, abstract = {

The Strebel point is a Teichmüller equivalence class in the Teichmüller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmüller equivalence class of the universal Teichmüller space under which the class is a Strebel point. As an application, we construct a Teichmüller equivalence class that is a Strebel point and that is not an asymptotically conformal class.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n1.9}, url = {http://global-sci.org/intro/article_detail/ata/4478.html} }
TY - JOUR T1 - A Sufficient Condition for Rigidity in Extremality of Teichmüller Equivalence Classes by Schwarzian Derivative AU - M. Yanagishita JO - Analysis in Theory and Applications VL - 1 SP - 130 EP - 135 PY - 2014 DA - 2014/03 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n1.9 UR - https://global-sci.org/intro/article_detail/ata/4478.html KW - Strebel points, the Schwarzian derivative, asymptotically conformal maps. AB -

The Strebel point is a Teichmüller equivalence class in the Teichmüller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmüller equivalence class of the universal Teichmüller space under which the class is a Strebel point. As an application, we construct a Teichmüller equivalence class that is a Strebel point and that is not an asymptotically conformal class.

M. Yanagishita. (2014). A Sufficient Condition for Rigidity in Extremality of Teichmüller Equivalence Classes by Schwarzian Derivative. Analysis in Theory and Applications. 30 (1). 130-135. doi:10.4208/ata.2014.v30.n1.9
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